V.  Benefits Analysis

Human Factors Issues

The Tire Pressure Monitoring Systems (TPMS) will provide notification to drivers that their tire pressure has dropped below the level recommended by the manufacturer.  However, driver response to this information may vary depending upon the nature of the information provided by the TPMS.  NHTSA believes that almost all drivers will respond in some manner to the warning, but the level of information presented to the driver by different display systems may result in different behavior by drivers. 

The indirect and hybrid measurement systems can only provide a warning light that tire pressure is low.  The direct measurement systems could display individual tire pressures and tell the driver which tire(s) are low.   Although individual tire pressures are not proposed to be required, this analysis assumes in Alternative 1a that all of the vehicles will be supplied with direct measurement systems that will display individual tire pressures because it will be helpful to drivers in terms of fuel economy, tread wear and safety.  This was done because of uncertainty regarding the exact nature of displays that manufacturers will install under Alternative 1.  Although there is clearly a greater potential for consumer information under Alternative 1, it is not clear to what extent manufacturers will take advantage of this. Therefore, Alternative 1a assumes a display with individual tire pressures, while Alternative 1b (and Alternatives 2 and 3) assume all vehicles will be equipped with only a warning light.     

We anticipate that drivers will react differently to the different amounts of information.   Some drivers will keep track of the individual tire pressures and will add pressure to their tires whenever necessary, say at 10 percent below placard, even before the warning is given.  These drivers will accrue more safety benefits and more benefits in terms of fuel economy and tread life than drivers that wait longer for a warning.  On the other hand, some drivers who currently check their own tires frequently enough to avoid significant under-inflation may start to rely on the TPMS to indicate under-inflation, rather than checking their tires frequently and filling them up whenever they were below the placard level.  We believe this would happen more often for an indirect or hybrid system, where only a warning light comes on when tire pressure goes below a specified threshold, rather than a direct system where individual tire pressures could be monitored continuously.  These drivers would actually accrue fewer safety, tread wear and fuel economy benefits than they did without the TPMS.  

The agency has little information that would help it estimate how a TPMS would affect overall driver tire maintenance behavior.  A survey question in the Bureau of Transportation Statistics Omnibus Survey of July 2001 asked 1,004 respondents "To what extent do you agree that an indicator light in your vehicle that warns the driver about under-inflation in any of the vehicle’s tires would allow you to be less concerned with routinely maintaining the recommended tire pressure?"  The responses were 40 percent to "a very great extent", 25 percent to "a great extent", 18 percent to "some extent", 7 percent to "a little extent", and 10 percent to "no extent".  Putting this information together with survey data from the tire pressure survey, where one-third of those surveyed indicated that they check their tire pressure at least once a month, indicates that some people would check their tire pressure more frequently.     

The agency has little information that would help it estimate what percent of drivers would put to use the information on individual tire pressures.  From the agency’s tire pressure survey, we found that about one-third of the interviewed drivers indicated that they check their tire pressure once a month or more frequently.  For Alternative 1a, we assume that one-third of the drivers would pay attention to the individual tire pressure information provided on a monitor and would refill their tires when they were 10 percent below the placard.  This means that if the average passenger car tire placard is 30 psi, we assume for Alternative 1a that one-third of the drivers would refill their tires when they get to 27 psi.  The other two-thirds of the drivers in Alternative 1a would refill their tires when the warning is given at 20 percent below placard, or 24 psi for the average passenger car.      

The second question is whether drivers, given a warning, will stop and inflate their tires back to the placard pressure.  We do not expect driver compliance with the TPMS telltale, which is amber or yellow, to be 100 percent.  We have found one study recently, although we don’t consider it reliable data, which addresses this issue.  Before finding this study we had assumed that 95 percent of drivers will fill the low tire(s) to make sure they don’t get a flat tire and be stranded somewhere.  Given just a telltale, the driver will probably need to check all the tires.  Given a reading of tire pressure on all four tires with a direct measurement system, the driver will know which tire(s) are low and need to be filled. 

NHTSA has recently received and will docket a study relating to the Cycloid Pump.  "Examining the Need for Cycloid’s Pump:  An Analysis of Attitudes and a Study of Tire Pressure and Temperature Relationships", December 7, 2001 by the University of Pittsburgh Department of Mechanical Engineering, Department of Industrial Engineering.

The study involves two parts, the first is an analysis indicating that the NHTSA tire pressure survey should have been adjusted to take into account that the tires were hot when tire pressures were taken, thus a higher percentage of the vehicles would have been under-inflated.  We initially considered this point but did not make adjustments because the tire pressure survey was done in February and tires tend to lose more air during the colder months.  We assumed that taking tire pressure when the tires were hot, but the air temperature for the month was cold would be offsetting factors. The agency is examining their analysis.   

The second part of the study and the more relevant part for this discussion is the survey they did of people’s attitudes.  The paper does not provide all of the data from the questions, but discusses some of them in the paper.  The survey is not a random survey of consumers representing a national picture.  The 225 respondents to the survey were:

1. classmates, faculty, and anyone they thought would respond to an E-mail survey

2. a group of consumers at a supermarket who were willing to participate.

One of the questions was:

Q21.  Would you respond to a dashboard warning light informing you that your tire pressure was low?

1. Yes

2. No.

219 out of 225 (97.3%) responded Yes.

Note that there were several questions before this one on how often do you check your tire pressure, when was the last time you checked your tire pressure, what is the recommended tire pressure in your vehicle, etc. These types of questions set up the respondents to thinking that tire pressure is an important topic worthy of checking out. 

While this is not a random sample, the question format may have biased the responses, and drivers actual deeds are often different from their telephone response, the response is overwhelming and leads some small credence to our own estimate that 95 percent of drivers will respond to a warning light.  

Another potential problem with an indirect system is with the reset button.  Most ABS-type indirect systems have a reset button that must be pushed whenever the tires have been rotated and perhaps when tires have been inflated.  There is the potential for the reset button to be misused, just to get the warning light to go out, before inflating the tires and then forgetting to inflate the tires.   In this case, the owners might not get future needed warnings that their tires are low.

In the Preliminary Economic Assessment we assumed that everyone filled their tires back up to the placard level and estimated the benefit of going from the level of pressure in the tire survey to the placard level.  Relatively conservative refill rates were assumed of 66.6 to 80 percent depending upon the information given to the driver.  These conservative refill rates, in some regards, were a proxy measure for several things.  First, some people will let their warning lights stay on until they think the tires are really low.  This assumes that they won’t trust the system.  Second, the tires are filled up and then lose air over time.  One could argue that the benefits of the system are going from the level of pressure in the tire survey to an average level of pressure between times the tires are refilled.   We estimated conservative refill rates to consider this possibility. 

Rather than use conservative refill rates as a proxy measure for two different factors, we have revised the analysis to examine the impacts of specifically estimating each of these two factors and determining how these estimates affect the benefits of the Alternatives.  

Assumptions:

1. Given a warning light goes on, 95 percent of people will check their tires and refill them back to the placard level.
2. Tires lose air at an average of 1 psi per month. 
3. In Alternative 1, for example, the warning has to be given at 20 percent below placard.  For passenger cars, assuming the average placard is 30 psi, the warning would be given at 24 psi.  The tires would be refilled at the time of the warning, and then would slowly lose air down to 29 psi at the end of month 1, 28 psi at the end of month 2, etc, until they reached 24 psi again when a new warning would be given.  Thus, the average steady state psi in this example is 27 psi [(30+29+28+27+26+25+24)/7].  For Alternatives 2 and 3, the warning must be given at 25 percent below placard.  Assuming the average placard is 30 psi, the warning must be given at 22.5 psi, and the average steady state psi in this example is 26.3 psi.  For Alternative 4, the warning must be given at 30 percent below placard.  Assuming the average placard is 30 psi, the warning must be given at 21 psi, and the average steady state psi in this example is 25.5 psi. 
4.  For Alternative 1a, we assume the display that will show individual tire pressures and that one-third of the drivers would pay attention to the display and fill up their tires every time they got to 10 percent below placard or 27 psi.  For these individuals that pay attention to the display, the average steady state psi in this example is 28.5 psi. We also assume that the other two-thirds of the drivers will not pay attention to the display and will fill up their tires when they get a warning at 24 psi.  Thus, their average steady state psi is 27 psi.  A weighted average of these is 27.5 psi (28.5*.333 + 27*.667). 
5. These same assumptions are used for the light truck fleet, except we assume that the average placard for light trucks is 35 psi.  The following table shows the results of the steady state assumptions for the different alternatives.  These mean that benefits are taken from the psi level at which vehicles would be getting a warning under each of the alternatives to the steady state assumptions of where the average fleet psi would be over time.   The benefits would then be multiplied by the 95 percent response rate to get the final estimated benefits.

	Steady State psi Level for Passenger Cars	Steady State psi Level for Light Trucks
Alternative 1a	27.5 psi	32.1 psi
Alternative 1b	27.0 psi	31.5 psi
Alternative 2	26.3 psi	30.6 psi
Alternative 3	26.3 psi	30.6 psi
Alternative 4	25.5 psi	29.8 psi

Skidding and Loss of Control

For loss of control crashes, speed is the most critical factor.  Excessive speed alone can cause a loss of control in a curve or in a lane change maneuver.  Tread depth, inflation pressure of the tires, and road surface condition are the most notable of a long list of factors including vehicle steering characteristics and tire cornering capabilities that affect the vehicle/tire interface with the road.  In the Indiana Tri-Level Study, under-inflation was not considered a contributing factor to a crash when there was high speed involved.  It was only considered when the tires were significantly under-inflated.  Still, it is hard to know whether correcting this one problem area could result in the collision being avoided or reduced in severity.  That is one reason why under-inflation was never cited as the definite cause of a crash.  We tried to consider this by comparing under-inflation as a percentage of all of the probable causes in crashes. Certainly, reducing under-inflation is an important area and a move in the right direction.  However, it is difficult to determine what the effectiveness of increasing tire pressure would be on these crashes.  The following discussions describe how inflation pressure affects these crash types to the extent known. 

Skidding and/or loss of control in a curve

Low tire pressure, as a result of under-inflation, generates lower cornering stiffness because of reduced tire stiffness.  When the tire pressure is low, the vehicle wants to go straight and requires a greater steering angle to generate the same cornering force in a curve.  The maximum speed at which an off-ramp can be driven while staying in the lane is reduced by a few mph as tire inflation pressure is decreased.  An example provided by Goodyear shows that when all four tires are at 30 psi the maximum speed on the ramp was 38 mph, at 27 psi the maximum speed was 37 mph, and at 20 psi the maximum speed was 35 mph while staying in the lane.  Having only one front tire under-inflated by the same amount resulted in about the same impact on maximum speed.  But, the influence of having only one rear tire under-inflated by the same amount was only about one-half of the impact on maximum speed (a 1.5 mph difference from 30 psi to 20 psi). 

The agency also has run a series of tests to examine the issue of decreases in tire pressure on vehicle handling.  A 2001 Toyota 4-Runner was run through 50 mph constant speed/decreasing radius circles to see the effects of inflation pressure on lateral road holding.  Figure V-1 shows the results of lefthand turns plotted from 0 to 90 degrees handwheel angle for tire inflation pressures varied from 15 to 35 psi.  The data indicate to us that in on-ramps/off ramps, tire inflation pressure is a critical factor in vehicle handling.  The graph shows how much friction the vehicle can utilize, in terms of lateral acceleration (g’s), before it slides off the road.  The more lateral g’s the vehicle can utilize, the better it stays on the road.  So, if you are going around an off-ramp and need to turn the wheel 50 degrees at 50 mph, you can utilize 0.27 g’s at 15 psi, or you can utilize 0.35 g’s at 30 psi. 

Skidding and/or loss of control in a lane change maneuver

In a quick lane change maneuver, under-inflated tires result in a loss of stiffness, causing poor handling.  Depending upon whether the low tire(s) are on the front or rear axle impacts the vehicle’s sensitivity to steering inputs, directional stability, and could result in a spin out and/or loss of control of the vehicle. 

Skidding and/or loss of control benefits estimate

In Chapter IV, we estimated a target population for skidding and loss of control crashes for under-inflated tires of 247 fatalities, 23,100 injuries and 53,130 property damage only crashes.  The agency assumes that 95 percent of drivers will fill their tires back to placard pressure.   

It is difficult to determine the effectiveness estimate, what percent of the crashes would be avoided by just improving low tire pressure. For this analysis, we assume 20 percent effectiveness to go to the steady state condition, although it could potentially be much higher.  Thus, the benefits by Alternative are shown in Table V-1.  An example calculation for Alternative 1 fatalities is 46 (247*.95*.20*.99 to account for one percent current compliance). 

Table V-1
Impacts for Skidding/Loss of Control Crashes

	PDO	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Non-Fatal Inj. Total	Fatal
Alt. 1(a)	-9,994	-3,725	-415	-177	-17	-11	-4,345	-46
Alt. 1(b)	-9,994	-3,725	-415	-177	-17	-11	-4,345	-46
Alt. 2	-9,104	-3,394	-378	-161	-15	-10	-3,958	-42
Alt. 3	-9,994	-3,725	-415	-177	-17	-11	-4,345	-46
Alt. 4	-6,478	-2,415	-269	-115	-11	-7	-2817	-30

Four things should be noted about Table V-1.  First, there are property damage only benefits.  However, these benefits are not discussed later in the analysis since they result in saving less than $0.10 per vehicle over its lifetime.  Second, the benefits are the same for Alternative 1(a) as they are for Alternative 3.  This reflects the finding that the levels of under-inflation in the Indiana Tri-Level study were higher than 25 percent to have under-inflation reported as a probable cause.  Thus, all of the vehicles would have gotten a warning whether they were 20 percent below placard or 25 percent below placard.  Theoretically it would be better to get the warning earlier under Alternative 1 at 20 percent below placard, rather than waiting until 25 percent below placard, but we could not distinguish this benefit. Third, the benefits for Alternative 2 are 8.9 percent less than the benefits for Alternative 3 to account for the vehicles that could not identify when all four of the tires are 25 percent below placard (8.9 derived from Table III-2 (d) average of 10% x 70% for passenger cars and 12.9% x 84% for light trucks). Fourth, the benefits for Alternative 4 are much less, since the indirect system gives a warning much less often at 30 percent differential.   

Stopping Distance

Tires are designed to maximize their performance capabilities at a specific inflation pressure.  When tires are under-inflated, the shape of the tire’s footprint and the pressure it exerts on the road surface are both altered.   This degrades the tire’s ability to transmit braking force to the road surface.   There are a number of potential benefits from maintaining the proper tire inflation level including reduced stopping distances, better handling of the vehicle in a curve or in a lane change maneuver, and less chance of hydroplaning on a wet surface, which can affect both stopping distance and skidding and/or loss of control.  

 The relationship of tire inflation to stopping distance is influenced by the road conditions (wet versus dry), as well as by the road surface composition.  Decreasing stopping distance is beneficial in several ways.  First, some crashes can be completely avoided by stopping quicker. Second, some crashes will still occur, but they occur at a lower impact speed because the vehicle is able to decelerate quicker during braking.

In Chapter III, a variety of stopping distance test results are discussed.  For the Preliminary Economic Assessment, NHTSA examined test results submitted by Goodyear Tire and Rubber Company as well as tests conducted at its own Vehicle Research Test Center (VRTC).   In tests conducted by Goodyear Tire and Rubber Company, significant increases were found in the stopping distance of tires that were under-inflated.   By contrast, tests conducted by NHTSA at their VRTC testing ground found only minor differences in stopping distance, and in some cases these distances actually decreased with lower inflation pressure.  The NHTSA tests also found only minor differences between wet and dry surface stopping distance.  It is likely that some of these differences were due to test track surface characteristics.  The NHTSA track surface is considered to be aggressive in that it allows for maximum friction with tire surfaces.  It is more representative of a new road surface than the worn surfaces experienced by the vast majority of road traffic.  The Goodyear tests may also have been biased in other ways.  Their basic wet surface tests were conducted on surfaces with .05" of standing water.  This is more than would typically be encountered under normal wet road driving conditions and may thus exaggerate the stopping distances experienced under most circumstances.     A general problem that applied to both data sets was that they measured stopping distance impacts for new tires only, while most vehicle miles are traveled on tires that are worn down to a level that is somewhere between full and minimal tread depths.  Since tread depth and tread profile can greatly influence both water retention and tire friction, this could have a significant impact on estimates of tire pressure on stopping distance. Generally speaking, the Goodyear test results implied a significant impact on stopping distance from proper tire pressure, while the NHTSA tests implied these impacts would be minor or nonexistent at lesser water depths.  The PEA estimated stopping distance impacts using the Goodyear data to establish an upper range of potential benefits.  A lower range of no benefit was implied based on the NHTSA test results.

In the PEA and in a subsequent memo to the docket (Docket No. 8572-81), NHTSA expressed concern regarding the adequacy of the currently available test data. In response, Goodyear conducted a new and comprehensive series of tests to evaluate the effects of tire inflation pressure on stopping distance.   The Goodyear tests were conducted using two different vehicles (Dodge Caravan and Ford Ranger), two different tires (P235/75R15 Wrangler and 215/70R15 Integrity), three inflation pressures (35, 28, and 20 psi), two tread depths (full tread and half tread), and three water depths (dry, .02 inches, and .05 inches).  In addition, the tests were run with ABS and without ABS. Stopping distances were measured from 45-5 mph.   A separate set of traction truck tests were also run to establish peak and slide coefficients of friction for these tires under similar circumstances but at speeds of 20, 40, and 60 mph.

NHTSA has examined the new data submitted by Goodyear and has found that it provides a much more comprehensive data set than was used previously for the PEA.   The variety of   water depths and tread depths are particularly important to resolving critical concerns with the initial data sets used in the PEA.  During the comment period, NHTSA contracted with the National Oceanic and Atmospheric Administration (NOAA) (See Docket No. 8572-167) to develop a data base that could be used to analyze the relative frequency of rainfall intensity in the U.S.  Based on these data, it now appears that the conditions which are likely to produce a surface water depth level of .05 inch, which was the basis for the original Goodyear tests, only occur about 10 percent of the time that it rains.  Thus, the addition of a second lesser water depth test of .02 inch was critical to measuring the impact on crashes that occur under most wet road conditions.   The new Goodyear data also confirm that tread depth has a significant influence on stopping distance.   Overall, the new test data seem to provide a comprehensive picture of the impacts of tire inflation on stopping distance, and are relatively free of the contradictions found in the earlier data sets.  For these reasons, NHTSA will base the final analysis on the new data set provided by Goodyear, rather than average the results of the two previous conflicting sets of data.        

Impact Speed/Injury Probability Model

In order to estimate the impact of improved stopping distance on vehicle safety, NASS-CDS data were examined to derive a relationship between vehicle impact speed (delta-V) and the probability of injury.  Following is a description of the derivation of this model. 

Data: From 1995-1999 CDS, all passenger vehicle occupants involved in crashes where at least one passenger vehicle used brakes.

Methodology: (1) The percent probability risk of MAIS 0, MAIS 1+, MAIS 2+, MAIS 3+,

MAIS 4+, MAIS 5+, and fatal injuries was calculated for each delta-V between 0 and 77 mph.   The percent probability risk of each MAIS j+ injury level at each delta-V i mph is defined as the number of MAIS j+ injury divided by the total number of occupants involved at i mph delta-V.  If j = 0 represents MAIS 0 injuries and j = 6 represents fatalities, the probability of injury risk can be represented by the following formula:

Where :

Note that p⁺_i,0 = percent probability risk of MAIS 0 injuries at i mph delta-V and p⁺_i,6 = percent probability risk of fatalities at i mph delta-V.  I_i,0 = the number of MAIS 0 injuries and I_i,6 the number of fatalities at i mph delta-V.

(2) The risk-prediction curve for each j injury level was derived using a mathematical modeling process.  The process used delta-V as the independent variable (i.e., predictor) and p⁺_i,j as the dependent variable and modeled all the data points (delta-V, percentage risk) for each j injury level.  For example, for MAIS 1+ injuries, the process used the data points: (0, p⁺_0,1), (1, p⁺_1,1), (2, p⁺_2,1), ..., (75, p⁺_75,1), (76, p⁺_76,1), (77, p⁺_77,1) to derive the MAIS 1+ risk curve.  Table V-2 shows all the risk-prediction formula.  These formulas were developed under two assumptions: a) no one was injured at 0 mph, i.e., P⁺_0,0 = 100 percent, and P⁺_0,j = 0 percent for j=1...6, and b) everyone was assumed to have at least MAIS 1 injuries for 36 mph and higher delta-V, i.e., p⁺_i,0 = 0 , for i >36 mph. This assumption was based on the injury distribution derived from 1995-1999 CDS. 

Table V-2
Injury Probability Risk Curve Formula

Injury Level	Risk-Prediction Formula
MAIS 0
MAIS 1+
MAIS 2+
MAIS 3+
MAIS 4+
MAIS 5+
Fatal (j=6)

(3) The percent probability risk p_i,j  was calculated for individual MAIS level.  For MAIS 0 (j=0) and fatal injuries (j=6), p_i,0 = p⁺_i,0 and p_i,6 = p⁺_i,6 .  The percentage risk for each MAIS 1 to MAIS 5 injury level is the difference between the two predicted risks. Thus, p_i,1 (risk of MAIS 1 at i mph delta-V) = p⁺_i,1 - p⁺_i,2, p_i,2 = p⁺_i,2 - p⁺_i,3, p_i,3 = p⁺_i,3 - p⁺_i,4, p_i,4 = p⁺_i,4 - p⁺_i,5, and p_i,5 = p⁺_i,5 - p⁺_i,6. 

(4) Adjusted total row percent risk to 100 percent.  Because of statistical measurement variation and predicting errors, the row risk percentages at some delta-Vs do not add to 100 percent.  To adjust to a total of 100 percent for these delta-Vs, an adjustment factor (f_i) is applied to every risk probability.  The adjustment factor is 100/(actual total percentage), i.e.,

 where j = 0...6.

The adjusted risk probabilities for i mph delta-V would be f_i * p_i,j.  For example, at 10 mph delta-V, f₁₀ = 100/85 = 1.1765.  The risk probability for MAIS 0 becomes 52.5 (= 44.6*1.1765) and MAIS 1 becomes 43.5 (= 37.0*1.1765).  These adjusted risk probabilities are higher than those predicted by the original curves listed in Table V-2.  However, the general shape of each curve does not alter significantly.  Table V-3 shows the adjusted percent probabilities of risk.  Note that cell probabilities were rounded to the nearest tenth.  Therefore the sum of the individual cells may not total exactly 100 percent.

Once this relationship was established, crash data from 1999 CDS and FARS were distributed across this matrix to establish a "base case" injury distribution.  This was done separately for 3 different groups of crashes stratified according to the speed limits on the roadways where crashes occurred.  The roadway stratification was selected because stopping distances are largely dependent on initial pre-braking travel speed, and speed limits were assumed to provide a reasonable stratification for this variable.  However, actual travel speeds differ from speed limits.  For this analysis, it was assumed that actual travel speeds were 5 mph higher than the mean speed limit in each category.  The 3 speed limit categories were 0-35mph, 36-50mph, and 51 mph and over.  The mean speed limits for each category were 30, 44, and 57.  There were only minor differences between speed limits for wet and dry surfaces, or for passenger cars and LTVs.  Therefore, the same average speed limit is used regardless of road surface or vehicle type.  Allowing for a 5 mph difference for travel speed, the three assumed average speeds that  represent the speed limit categories are 35, 49, and 62 mph.

Table V-3
Adjusted Percent Probabilities of Injury Risk

Delta-V (mph)	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
0	100.0	0.0	0.0	0.0	0.0	0.0	0.0	100.0
1	95.6	3.5	0.4	0.3	0.1	0.0	0.0	99.9
2	91.0	8.0	0.4	0.4	0.0	0.1	0.0	99.9
3	86.3	12.5	0.5	0.5	0.0	0.1	0.0	99.9
4	81.3	17.2	0.7	0.7	0.0	0.1	0.0	100.0
5	76.3	21.9	0.9	0.7	0.0	0.0	0.1	99.9
6	71.3	26.6	1.0	0.8	0.1	0.0	0.1	99.9
7	66.4	31.2	1.3	0.9	0.1	0.0	0.1	100.0
8	61.5	35.7	1.5	1.1	0.1	0.0	0.1	100.0
9	56.9	39.6	2.0	1.2	0.0	0.1	0.1	99.9
10	52.5	43.5	2.4	1.3	0.1	0.1	0.1	100.0
11	48.2	47.1	2.8	1.5	0.1	0.1	0.1	99.9
12	44.3	50.2	3.4	1.6	0.2	0.0	0.2	99.9
13	40.5	53.1	3.9	2.0	0.1	0.1	0.2	99.9
14	37.1	55.6	4.6	2.2	0.2	0.1	0.2	100.0
15	33.9	57.6	5.5	2.4	0.2	0.1	0.3	100.0
16	31.0	59.1	6.5	2.6	0.3	0.1	0.3	99.9
17	28.3	60.4	7.6	2.9	0.3	0.2	0.3	100.0
18	25.8	61.1	8.8	3.3	0.3	0.2	0.4	99.9
19	23.5	61.5	10.1	3.7	0.3	0.2	0.5	99.8
20	21.4	61.4	11.7	4.1	0.4	0.3	0.5	99.8
21	19.6	61.0	13.4	4.5	0.5	0.3	0.6	99.9
22	17.8	60.1	15.4	5.0	0.5	0.4	0.7	99.9
23	16.3	58.8	17.4	5.6	0.5	0.4	0.9	99.9
24	14.9	57.1	19.6	6.2	0.6	0.5	1.0	99.9
25	13.7	55.1	21.9	6.9	0.7	0.5	1.2	100.0
26	12.6	52.7	24.4	7.6	0.8	0.7	1.3	100.1
27	11.5	50.0	26.9	8.4	0.9	0.7	1.6	100.0
28	10.5	47.1	29.5	9.2	1.0	0.9	1.8	100.0
29	9.6	43.9	32.1	10.1	1.2	1.0	2.1	100.0
30	8.9	40.6	34.5	11.0	1.4	1.2	2.4	100.0
31	8.2	37.1	36.8	12.1	1.5	1.4	2.8	99.9
32	7.6	33.7	38.9	13.3	1.7	1.5	3.3	100.0
33	7.0	30.2	40.9	14.4	1.9	1.8	3.8	100.0
34	6.4	26.7	42.5	15.7	2.2	2.0	4.4	99.9
35	6.0	23.2	43.9	17.1	2.4	2.3	5.1	100.0
36	0.0	26.4	44.3	18.1	2.7	2.6	5.9	100.0
37	0.0	23.3	44.7	19.3	2.9	3.0	6.8	100.0
38	0.0	20.4	44.7	20.4	3.3	3.4	7.8	100.0
39	0.0	17.8	44.3	21.5	3.6	3.8	9.0	100.0
40	0.0	15.5	43.5	22.5	4.0	4.2	10.3	100.0
41	0.0	13.4	42.5	23.3	4.3	4.7	11.8	100.0
42	0.0	11.6	41.1	24.0	4.6	5.3	13.4	100.0
43	0.0	10.0	39.5	24.4	4.9	5.9	15.3	100.0
44	0.0	8.5	37.7	24.8	5.2	6.4	17.4	100.0
45	0.0	7.3	35.7	24.9	5.5	6.9	19.7	100.0
Table V-3 Adjusted Percent Probabilities of Injury Risk, Cont.
46	0.0	6.3	33.6	24.7	5.7	7.5	22.2	100.0
47	0.0	5.3	31.5	24.4	5.8	8.0	25.0	100.0
48	0.0	4.5	29.4	23.7	6.0	8.5	27.9	100.0
49	0.0	3.9	27.2	22.9	6.0	8.9	31.1	100.0
50	0.0	3.3	25.1	21.9	6.0	9.2	34.5	100.0
51	0.0	2.8	23.0	20.8	6.0	9.4	38.0	100.0
52	0.0	2.4	21.0	19.6	5.8	9.6	41.6	100.0
53	0.0	2.0	19.2	18.2	5.6	9.6	45.4	100.0
54	0.0	1.7	17.4	16.9	5.3	9.5	49.2	100.0
55	0.0	1.4	15.8	15.5	5.0	9.3	53.0	100.0
56	0.0	1.2	14.2	14.1	4.7	9.1	56.7	100.0
57	0.0	1.0	12.8	12.8	4.3	8.7	60.4	100.0
58	0.0	0.9	11.4	11.5	3.9	8.3	64.0	100.0
59	0.0	0.7	10.3	10.2	3.6	7.7	67.5	100.0
60	0.0	0.6	9.2	9.1	3.2	7.2	70.7	100.0
61	0.0	0.5	8.2	8.0	2.9	6.6	73.8	100.0
62	0.0	0.4	7.4	7.0	2.5	6.1	76.6	100.0
63	0.0	0.4	6.5	6.1	2.2	5.6	79.2	100.0
64	0.0	0.3	5.8	5.3	2.0	5.0	81.6	100.0
65	0.0	0.3	5.1	4.6	1.7	4.5	83.8	100.0
66	0.0	0.2	4.6	4.0	1.4	4.0	85.8	100.0
67	0.0	0.2	4.0	3.5	1.2	3.6	87.5	100.0
68	0.0	0.2	3.5	3.0	1.1	3.1	89.1	100.0
69	0.0	0.1	3.2	2.5	0.9	2.8	90.5	100.0
70	0.0	0.1	2.8	2.2	0.8	2.4	91.7	100.0
71	0.0	0.1	2.5	1.8	0.7	2.1	92.8	100.0
72	0.0	0.1	2.2	1.5	0.6	1.8	93.8	100.0
73	0.0	0.1	1.9	1.3	0.5	1.6	94.6	100.0
74	0.0	0.1	1.7	1.1	0.4	1.4	95.3	100.0
75	0.0	0.1	1.4	1.0	0.3	1.2	96.0	100.0
76	0.0	0.0	1.4	0.8	0.2	1.1	96.5	100.0
77	0.0	0.0	1.2	0.7	0.2	0.9	97.0	100.0

Separate target populations were also derived for passenger cars and LTVs, and for crashes that occur on wet and dry pavement.  These distinctions were necessary because stopping distance is strongly influenced by pavement conditions and vehicle characteristics.  In addition, LTVs have significantly different levels of under-inflation than passenger cars and this impacts calculations of delta-V reductions.  Note that the presence or absence of anti-lock brakes also has a significant influence on stopping distance. However, because reliable data on the presence of these systems is not included in crash databases, these differences will be accounted for at a different stage of the analysis. A total of 12 separate target population cells were thus produced.  The fatalities and injuries for each cell are summarized in Table V- 4 for passenger cars and Table V-5 for LTVs.  Table V-6 summarizes the target populations across all passenger vehicles.  

Table V-4
Passenger Vehicle Occupants in Crashes Where
at Least One Passenger Car Used Brakes
1995-1999 CDS, Annual Average

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
WET
0-35mph	85606	75611	6775	3101	275	163	362	171892
36-50mph	54150	68246	6886	3007	249	161	361	133060
51+mph	22209	23586	2391	1064	94	70	146	49560
DRY
0-35mph	195969	180663	17018	7616	654	438	965	403322
36-50mph	218895	219066	20463	9123	860	480	1273	470158
51+mph	58407	73930	13700	5237	554	423	959	153208
Total	635236	641101	67233	29147	2685	1735	4064	1381201

Table V-5
Passenger Vehicle Occupants in Crashes Where
at Least One LTV Used Brakes
1995-1999 CDS, Annual Average

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
WET
0-35mph	23345	27243	2621	1156	101	66	135	54668
36-50mph	34549	42404	3664	1729	121	95	212	82774
51+mph	8183	9810	1535	649	79	66	182	20503
DRY
0-35mph	98640	99100	11291	4800	466	293	699	215290
36-50mph	87072	98763	12016	4985	460	341	911	204547
51+mph	44147	50883	9399	3687	412	321	726	109575
Total	295936	328204	40526	17006	1639	1182	2865	687358

Table V-6
Passenger Vehicle Occupants in Crashes Where
at Least One Vehicle Used Brakes
1995-1999 CDS, Annual Average

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
WET
0-35mph	108951	102854	9396	4257	376	229	497	226561
36-50mph	88699	110650	10551	4736	370	256	573	215835
51+mph	30392	33396	3926	1712	173	136	328	70064
DRY
0-35mph	294609	279763	28310	12416	1120	731	1664	618612
36-50mph	305966	317828	32478	14108	1320	821	2184	674705
51+mph	102554	124813	23098	8924	966	744	1684	262783
Total	931172	969305	107759	46153	4325	2917	6930	2068560

Preventable Crashes

The impact of small reductions in stopping distance will, in most cases, result in a reduction in the impact velocity, and hence the severity, of the crash.  However, in some cases, reduced stopping distance will actually prevent the crash from occurring.  This would result, for example, if the braking vehicle were able to stop just short of impacting another vehicle instead of sliding several more feet into the area it occupied.

The benefits that would accrue from preventable crashes would only impact that portion of the fleet that:

1. Has low tire pressure, and

2. Would be notified by the TPMS

3. Is driven by drivers who will respond to the warning

Data from NHTSA’s tire pressure survey (discussed in Chapter III) indicate that 74 percent of the on-road fleet has at least one tire that is under-inflated.  For these vehicles, notification of this under-inflation would not be given until the system is triggered. For example, under Alternative 1, it is estimated that direct TPMS will trigger at roughly 20% below placard pressure, or roughly 6 psi for passenger cars and 7 psi for trucks.  The portion of the vehicle fleet that is below these levels will potentially experience some reduction in crash incidence due to improved stopping distance.   Data from NHTSA’s tire pressure survey indicate that 36 percent of passenger cars and 40 percent of LTVs have at least one tire that is 20 percent or more below recommended placard pressure.  However, in order to experience this reduction in stopping distance, the driver must respond to the warning.  NHTSA has no data to indicate what portion of drivers will take action in response to this warning.  For this analysis, it will be assumed that 95 percent would respond to a warning and refill their tires back to the placard level. 

The portion of crashes that would actually be preventable is unknown.  However, an estimate can be derived from relative stopping distance calculations for vehicles that were involved in crashes.  The average stopping distance was calculated for the existing crash-involved vehicle fleet, and for that fleet if they had correct tire inflation pressure.  The method used to calculate these stopping distances is described later in this section of the analysis. The results indicate that the existing passenger car fleet would, on average, experience a stopping distance of 86.5 feet, while the crash-involved LTV fleet experienced an average stopping distance of 91.9 feet.  These differences between passenger car and LTV stopping distances reflect the distribution of injuries by speed and road conditions for each vehicle type.  By contrast, the average stopping distance for passenger cars with correctly inflated tires would be 85.2 feet, while for LTVs it would be 90.7 feet.

In theory, current crashes occur under a variety of stopping distances but if these distances were shortened due to improved inflation pressure then a portion of these crashes would be prevented.  Crashes could be prevented over a variety of travel speeds and braking distances.  For example, a vehicle might be able to avoid an intersection crash by slowing quickly enough to miss a speeding vehicle running a red light.  In an angular head-on crash, better braking could reduce the chance of two vehicles striking their corners, given that crash avoidance maneuvers are also taking place.  An example for rear impacts could involve sudden braking to avoid a vehicle swerving to cross lanes on an interstate highway.  We anticipate that a large portion of the fatality and serious injury benefits for crash avoidance would occur in intersection crashes, since both vehicles are moving at high speeds, and a small change in braking efficiency could result in the avoidance of a high-impact crash. 

NHTSA does not have data that indicate average stopping distance in crashes.  Under these circumstances, it is not unreasonable to assume that crashes are equally spread over the full range of stopping distances.   Under this assumption, the change in stopping distance under proper inflation conditions can be used as a proxy for the portion of crashes that are preventable.  With equal distribution of crashes across all stopping distances, the portion of crashes that occur within the existing stopping distance that exceeds the stopping distance with correct pressure represents the portion of crashes that are preventable.  For passenger cars, this portion is (86.5-85.2)/86.5 or 1.38 percent of all current crashes.  For LTVs, this portion is (92.0-90.7)/92.0 or 1.36 percent.

Benefits from preventable crashes were thus calculated as follows:

Where,

The results of this analysis are shown for passenger cars under Alternative 1 in Table V-7.  The combined results for all vehicles under Alternative 1 are shown in Table V-8, and for Alternatives 2, 3 and 4 in Tables V-9, V-10 and V-11.  Note that these results have been adjusted to reflect a small amount of overlap that occurred in the separate examination of passenger car and LTV crashes.  An adjustment factor of .968 was applied to account for this overlap.  This factor was derived by comparing the sum of the two separate crash counts to a total count based on all passenger vehicles. These estimates were also adjusted to reflect the impact of threshold braking. This concept is discussed in detail in the following section on non-preventable crashes.

The benefits from preventable crashes, shown in Tables V-7, 8, 9,10 and 11, were assumed to occur over all crash types and severities.  This assumption recognizes that there are a variety of crash circumstances for which marginal reductions in stopping distance may prevent the crash from occurring.  Crash prevention may be more likely under some circumstances than others.  For example, it is possible that a larger portion of side impacts might be prevented than head-on collisions.  In side impacts where vehicles are moving perpendicular to each other, improved braking by one vehicle reduces the speed at which it enters the crash zone and potentially allows the second vehicle to move through the crash zone, thus avoiding the impact.  In a head-on collision, both vehicles are moving toward the crash and a reduction in stopping distance for one vehicle may be less likely to avoid a high-speed crash than in the case discussed above for side impacts.  Further, if a separate analysis were conducted for different crash types and severities, the portion of crashes prevented would be greater for crashes at higher speeds.  However, NHTSA does not have sufficient information to conduct a separate analysis of each crash circumstance and has used an overall estimate across all crash types instead. 

Note that this analysis only addresses injury crashes.  Property damage only crashes would also be impacted by proper tire inflation.  However, given that these are the least serious category of crashes, and that the average stopping distance impact in these preventable crashes is only about one foot, it is likely that the property damage only crashes prevented would involve very low speed crashes.  These low speed crashes would have very low levels of costs involved.  The agency does not have cost data specific to these low speed property damage crashes.    

Table V-7
Potential Benefits from Preventable Crashes,
Passenger Cars Adjusted for Properly Inflated Vehicles,
20% Notification Level, 95% Response Rate, and Overlap

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	336	-297	-27	-12	-1	-1	-1
36-50mph	213	-268	-27	-12	-1	-1	-1
51+mph	87	-93	-9	-4	0	0	-1
DRY
0-35mph	770	-710	-67	-30	-3	-2	-4
36-50mph	860	-861	-80	-36	-3	-2	-5
51+mph	230	-291	-54	-21	-2	-2	-4
Total	2496	-2519	-264	-115	-11	-7	-16

NOTE:  Negative signs indicate reductions in injury levels.

Table V-8a
Potential Benefits from Preventable Crashes, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles,
Delta-V Distribution, 95% Response Rate, Overlap, and Braking Threshold
Alternative 1a

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	373	-354	-32	-15	-1	-1	-2
36-50mph	309	-386	-37	-16	-1	-1	-2
51+mph	105	-115	-14	-6	-1	0	-1
DRY
0-35mph	551	-525	-53	-23	-2	-1	-5
36-50mph	570	-593	-61	-26	-2	-2	-7
51+mph	194	-235	-44	-17	-2	-1	-5
Total	2101	-2208	-241	-104	-10	-6	-22

NOTE:  Negative signs indicate reductions in injury levels.

Table V-8b
Potential Benefits from Preventable Crashes, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles,
Delta-V Distribution, 95% Response Rate, Overlap, and Braking Threshold
Alternative 1b

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	349	-331	-30	-14	-1	-1	-2
36-50mph	289	-361	-34	-15	-1	-1	-2
51+mph	98	-108	-13	-6	-1	0	-1
DRY
0-35mph	516	-491	-50	-22	-2	-1	-5
36-50mph	533	-555	-57	-25	-2	-1	-6
51+mph	182	-220	-41	-16	-2	-1	-5
Total	1966	-2066	-225	-97	-9	-6	-21

Table V-9
Potential Benefits from Preventable Crashes, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, and Threshold Braking
Alternative 2

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	203	-188	-17	-8	-1	0	-1
36-50mph	155	-194	-19	-8	-1	0	-1
51+mph	56	-60	-7	-3	0	0	-1
DRY
0-35mph	284	-267	-27	-12	-1	-1	-2
36-50mph	300	-309	-31	-13	-1	-1	-3
51+mph	95	-117	-22	-8	-1	-1	-2
Total	1092	-1135	-122	-53	-5	-3	-11

NOTE:  Negative signs indicate reductions in injury levels.

Table V-10
Potential Benefits from Preventable Crashes, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, and Threshold Braking
Alternative 3

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	233	-221	-20	-9	-1	0	-1
36-50mph	192	-239	-23	-10	-1	-1	-1
51+mph	65	-72	-8	-4	0	0	-1
DRY
0-35mph	343	-326	-33	-14	-1	-1	-3
36-50mph	355	-369	-38	-16	-2	-1	-4
51+mph	120	-146	-27	-10	-1	-1	-3
Total	1307	-1372	-149	-64	-6	-4	-14

Table V-11
Potential Benefits from Preventable Crashes,
All Passenger Vehicles Adjusted for Properly Inflated Vehicles,
Delta-V Distribution, 95% Response Rate, and Overlap and Threshold Braking
Alternative 4

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	123	-115	-10	-5	0	0	-1
36-50mph	97	-121	-12	-5	0	0	-1
51+mph	34	-37	-4	-2	0	0	0
DRY
0-35mph	175	-166	-17	-7	-1	0	-2
36-50mph	184	-190	-19	-8	-1	0	-2
51+mph	60	-73	-14	-5	-1	0	-2
Total	672	-701	-76	-33	-3	-2	-7

Non-Preventable Crashes

In the vast majority of crashes, small changes in stopping distance will not prevent the crash, but will reduce the speed at impact and thus the severity of the crash.  As noted above, 1.38 percent of braking passenger cars and 1.36 percent of braking trucks could have avoided crashes with proper tire inflation.  The remaining 98.6 percent of passenger car and LTV crashes would still occur, but at a reduced impact speed.  To estimate the impact of reduced crash speeds, changes in stopping distance will be estimated and used as inputs to recalculate impact speeds for the population of non-preventable crashes.  These changes in impact speeds will then be used to redefine the injury profile of this crash population shown in Table V-3, and safety benefits will be calculated as the difference between the existing and the revised injury profiles.  

Stopping Distance

Stopping distance can be computed as a function of initial velocity and tire friction.  The formula for computing stopping distance is as follows:

Where:

About a third of all passenger vehicles sold in the U.S. do not have anti-lock brakes, although the portion is higher in the on-road fleet.  For these regular braking systems, the term for anti-lock brake efficiency (E) would not be used.  

Calculating Mu

The value of Mu is dependent on surface material (concrete, asphalt, etc.), surface condition (wet vs. dry), inflation pressure, and initial velocity.  Based on data provided by The Goodyear Tire and Rubber Company in response to the NPRM, NHTSA developed a  model that predicts Mu based on Vi and inflation pressure.  Separate models were developed for Mu at both peak (the maximum level of Mu achieved while the tire still rotates under braking conditions) and slide (the level of Mu achieved when tires cease to rotate while braking (i.e., skid)).    The peak models are used for vehicles with antilock brake systems.  The slide models are appropriate for vehicles with non-antilock brake systems.  The models are as follows:

For Wet surface conditions

For Dry surface conditions

Where:

Note that the wet surface condition model is based on 2 separate models.  One was derived from the Goodyear tests conducted with .05 inches of water, and one with .02 inches of water.  As noted previously, data from NOAA (See Docket No. 8572-167) indicate that only about 10 % of rainfall events occur at rates that would be necessary to produce .05 inches of water on road surfaces.  The 2 wet condition models were therefore weighted to produce a single model based on weights of 90% for the .02 inch model and 10% for the .05 inch model

Mu Surface Adjustments

The above formulae were derived from tests conducted on a Traction Truck surface (this is a specific surface calibrated to specifications of the companies OEM customers).  In order to relate them to real world surfaces, predicted values from the formulas were compared to actual test results obtained using the same tires mounted on vehicles.  The vehicles used were a Dodge Caravan for the 215/70R15 Integrity tire, and a Ford Ranger for the P235/75R15 Wrangler.  Generally, the Integrity tests were intended to represent passenger cars while the Wrangler tests were intended to represent LTV performance.  The tests were all run with an initial velocity of 45 mph, with braking measured down to 5 mph.  Goodyear did not record data to a complete stop.  In order to compare the predicted stopping distance results from the Mu regressions to real world results, braking distance was measured using the following equation:

Where:

 This is a simple modification of the formula previously discussed for stopping distance.  The Vii term is necessary to adjust for the 5 mph braking limit in the vehicle tests.    Mu peak and slide values were estimated for each of the 3 psi levels used in the Goodyear vehicle tests at 45 mph.   The resulting predicted BDs were then compared to the actual braking distance found in the corresponding vehicle tests.  The actual BDs were weighted to reflect an average of the full and half tread tests.  Weighting factors for the actual BDs were derived from tread depth data obtained in NHTSA’s tire inflation survey.  Full tread for the Integrity tire (assumed to represent passenger tires) was 10/32 inch and half tread was 5/32. For the Wrangler tire (assumed to represent LTVs), full tread was 13/32 and half tread was 6.5/32).   Data from the NHTSA survey indicate that about 2/3 of all vehicle tires had tread depths more similar to the ½ tread level and about 1/3 had tread depths more similar to the full depth levels.

A comparison of the predicted and actual weighted BDs indicated close similarity across the three different psi levels.  Therefore, factors were averaged across the 3 levels.  However, they differed significantly by tire type, surface condition, and for peak vs. slide. Overall, the results of this comparison indicate that factors of from roughly 1.3 to 1.8 are required to adjust the stopping distances predicted using the Mu based algorithms.  The Wrangler factors were applied to LTV estimates and the Integrity factors were applied to passenger car estimates.  Wet and dry factors were also applied to their corresponding cases.  Peak factors were applied to vehicles with antilock brakes, while slide factors were applied to vehicles without antilock brakes.  The factors used are summarized in Table V-12.

Table V-12
Vehicle Surface Adjustment Factors

	Wrangler		Integrity
Wet Peak	1.8379		1.7246
Wet Slide	1.4856		1.2709
Dry Peak	1.7586		1.6260
Dry Slide	1.5954		1.5203

Anti-lock and Normal Braking Systems

Roughly 2/3 of all passenger vehicles sold in the U.S. have anti-lock brakes, but the portion is smaller in the on-road fleet.  For vehicles with anti-lock brake systems, Mp is used to calculate stopping distance because it represents the peak controlled braking force that anti-lock brakes attempt to maintain.  For vehicles with regular brake systems, Ms is used because it represents the level of friction encountered under normal braking by most drivers without assistance from anti-lock brakes.  Also, for these regular braking systems, the term for anti-lock brake efficiency (E) would not be used.  

Delta-V

Changes in stopping distances were then used to calculate the decrease in crash forces (measured by delta-V) that would occur due to the decrease in striking velocity of the vehicle.  The formula used to calculate striking velocity is:

Where:

In this case, V_(d) is a measure of the speed at which the vehicle with under-inflated tires would be traveling when it reaches the distance at which it would have stopped had its tires been correctly inflated (d).   Deceleration (a) is calculated for the vehicle with under-inflated tires.  The derived formula for deceleration is:

Since V = 0 at d, the formula becomes:

and will be ignored from this point on)

The distance over which a is calculated is the stopping distance for the vehicle with under-inflated tires.  This will be designated as SDu.  The formula thus becomes:

Where:

The striking velocity is then expressed in mph by multiplying by 1/ 5280 ft.*3600 sec. hour.  The delta-V experienced by each vehicle would be dependent on vehicle mass.  For this analysis, the mass of each vehicle was assumed to be equal, giving a delta-V of 1/2 V(d) for each vehicle or:

Where:

The base case target population represents the injury profile that results from the fleet of passenger vehicles that were on the road at that time.  In order to determine the inflation pressure that exists in that fleet, NHTSA conducted a survey of both recommended and actual inflation pressures on vehicles.   Details of that survey are discussed elsewhere in this analysis. The results of the survey indicate that 74% of all passenger vehicles are driven with under-inflated tires.   However, because TPMS would not notify drivers of low pressure until it dropped 20% or 25% below placard, no stopping distance benefits would accrue to vehicles with smaller tire pressure deficits.   Weighting factors were derived from the tire pressure survey to represent the affected population under each alternative.  For Alternative 1, these weights were drawn from the population that had at least one tire 20% or more under-inflated.  For Alternative 2 and 3, these weights were drawn from the population that had at least one tire 25% or more under-inflated.  In the case of Anti-lock Brake systems under Alternative 2, the population was also restricted to cases where the maximum inflation pressure of any tire exceeded the minimum pressure by at least 25%.  The distribution of each level of under-inflation is shown in Table V-13 for all 4 Alternatives. 

For Alternative 4, a different set of restrictions was used for anti-lock and non-anti-lock brake vehicles.  For anti-lock brake equipped vehicles, the population use based on the algorithm that describes tire pressure loss in current indirect systems.  This essentially measures the difference in the sum of two diagonal paired sets of tires divided by the average inflation pressure of all 4 tires.  In current systems axel speed in used as a proxy for tire pressure.  Tire pressure was used for these calculations under the assumption that axel speed does correlate well with tire pressure.  The population for anti-lock brake equipped vehicles was restricted to cases where the result of the pressure difference measured by the algorithm equaled or exceeded 30 percent.

For non-anti-lock vehicles, weights were drawn from the population that had at least one tire 30% or more under-inflated.

Table V-13
Percent of Vehicles Under-inflated Within Notification Levels

Alternative 1			Alternatives 2 and 3				Alternative 4
20% or more below Placard pressure			25% or more below Placard pressure
			Anti-lock Brakes (A2 only)		A3 +Non-Anti-lock Brakes in A2		Anti-lock 30% or more below Average		Non Anti-Lock 30% or more below Placard
Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated	Percent Under-Inflated
Pressure (psi)	PCs	LTVs	PCs	LTVs	PCs	LTVs	PCs	LTVs	PCs	LTVs
-1	3.5%	1.2%	19.0%	14.6%	0.2%	0.2%	15.94%	12.33%	0.00%	0.13%
-2	8.8%	5.4%	13.1%	12.0%	7.4%	4.9%	12.97%	13.28%	5.50%	3.93%
-3	13.1%	8.1%	14.4%	10.4%	11.2%	6.0%	15.64%	9.11%	10.43%	5.20%
-4	13.5%	11.5%	12.0%	9.6%	11.8%	8.2%	12.97%	10.25%	11.18%	6.84%
-5	15.3%	11.7%	10.5%	10.0%	13.7%	8.4%	10.99%	10.25%	12.93%	7.60%
-6	12.2%	14.8%	7.5%	10.0%	12.3%	13.1%	7.33%	9.87%	11.26%	11.28%
-7	10.3%	11.1%	6.7%	6.7%	12.2%	11.2%	6.44%	6.07%	11.68%	9.13%
-8	7.4%	8.8%	4.9%	6.6%	9.7%	11.2%	5.15%	7.21%	10.01%	9.89%
-9	5.4%	6.5%	3.7%	4.0%	7.4%	8.5%	4.16%	5.12%	8.51%	8.75%
-10	3.5%	5.6%	2.2%	4.0%	4.8%	7.6%	2.08%	3.98%	6.17%	7.86%
-11	2.3%	3.8%	1.6%	3.6%	3.1%	5.1%	1.39%	2.47%	4.00%	6.84%
-12	1.8%	2.6%	1.8%	2.2%	2.4%	3.5%	2.18%	2.09%	3.17%	4.69%
-13	0.9%	1.6%	1.1%	1.3%	1.3%	2.2%	1.29%	1.90%	1.67%	3.17%
-14	0.5%	1.2%	0.4%	1.2%	0.6%	1.6%	0.30%	1.52%	0.83%	2.28%
-15	0.6%	0.7%	0.4%	0.4%	0.8%	0.9%	0.30%	0.57%	1.08%	1.27%
-16	0.3%	1.2%	0.3%	0.7%	0.4%	1.7%	0.40%	0.95%	0.50%	2.41%
-17	0.1%	0.7%	0.2%	0.4%	0.2%	1.0%	0.20%	0.38%	0.25%	1.39%
-18	0.1%	0.5%	0.1%	0.1%	0.1%	0.7%	0.10%	0.00%	0.17%	1.01%
-19	0.0%	0.3%	0.0%	0.1%	0.0%	0.4%	0.00%	0.38%	0.00%	0.63%
-20	0.1%	0.3%	0.1%	0.2%	0.1%	0.4%	0.10%	0.38%	0.08%	0.63%
-21	0.1%	0.3%	0.0%	0.2%	0.1%	0.4%	0.00%	0.38%	0.08%	0.51%
-22	0.1%	0.2%	0.1%	0.1%	0.1%	0.3%	0.10%	0.00%	0.17%	0.38%
-23	0.0%	0.3%	0.0%	0.4%	0.0%	0.4%	0.00%	0.19%	0.00%	0.63%
-24	0.1%	0.3%	0.1%	0.1%	0.1%	0.4%	0.00%	0.19%	0.17%	0.51%
-25	0.0%	0.2%	0.0%	0.1%	0.0%	0.3%	0.00%	0.00%	0.00%	0.38%
-26	0.1%	0.1%	0.0%	0.1%	0.1%	0.2%	0.00%	0.19%	0.08%	0.25%
-27	0.0%	0.2%	0.0%	0.1%	0.0%	0.3%	0.00%	0.00%	0.00%	0.38%
-28	0.0%	0.1%	0.0%	0.0%	0.0%	0.1%	0.00%	0.00%	0.00%	0.13%
-29	0.1%	1.0%	0.0%	0.7%	0.1%	1.3%	0.00%	0.95%	0.08%	1.89%
Total	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%

As noted previously, the value of Mu in the formula for stopping distance is dependent on inflation levels.  For each speed limit category, a set of delta-Vs corresponding to each under-inflation level was calculated.  In each case, an average placard pressure of 30 psi was assumed for passenger cars.  For LTVs, an average pressure of 35 was assumed.   The rates of under-inflation in Table V-13 were used to weight the change in delta-V that results from each corresponding psi under-inflation level to an overall weighted average change across all levels.  The resulting changes in delta-V are summarized in Table V-14 for each passenger car and LTV target population category for ABS systems, non-ABS systems and combined systems, based on weighting factors representing the relative portion of the vehicle fleet that has Anti-lock brakes.  Similar results are summarized for Alternative 2 in Table V-15, and for Alternative 3 in Table V-16 and for Alternative 4 in Table V-17.  Note that these estimates do not reflect any impact for vehicles with inflation levels that are less than the assumed set point for the TPMS system.  For Alternative 1, this analysis assumes a set point of 20 percent below the placard pressure, or 6 psi based on the assumption of a 30 psi recommended pressure.  Benefits would only accrue to those tires that are more than 6 psi beneath their recommended pressure.  For LTVs, benefits would accrue for those tires that are more than 7 psi beneath their recommended pressure.   Alternatives 2 and 3 assume a set point of 25% below placard for non-anti-lock brake systems and this results in higher average delta-V changes for these systems under Alternative 2 and 3 than Alternative 1, due to the higher level of potential improvement within this more limited population of vehicles.  However, for vehicles with anti-lock brakes, the systems would only operate in cases where the highest tire pressure exceeded the lowest tire pressure by 25% or more, and this less rigorous level of notification results in a lower average delta-V change under Alternative 2 than under Alternative 1.

Table V-14
Weighted Average Reductions In Delta-V
from Improved Tire Inflation Pressure
Alternative 1

		Anti-lock	Non-Anti-lock	Combined
Passenger Cars:
Wet Pavement
	0-35mph	2.685	3.141	2.836
	36-50mph	3.820	4.785	4.139
	51+mph	4.883	6.720	5.489
Dry Pavement
	0-35mph	2.127	1.240	1.834
	36-50mph	3.014	1.705	2.582
	51+mph	3.823	2.079	3.248
LTVs:
		Anti-lock	Non-Anti-lock	Combined
Wet Pavement
	0-35mph	2.991	3.485	3.154
	36-50mph	4.254	5.294	4.597
	51+mph	5.436	7.406	6.086
Dry Pavement
	0-35mph	2.379	1.393	2.054
	36-50mph	3.371	1.915	2.891
	51+mph	4.138	2.337	3.544

Table V-15
Weighted Average Reductions In Delta-V
from Improved Tire Inflation Pressure
Alternative 2

		Anti-lock	Non-Anti-lock	Combined
Passenger Cars
Wet Pavement
	0-35mph	2.326	3.342	2.661
	36-50mph	3.309	5.092	3.897
	51+mph	4.230	7.151	5.194
Dry Pavement
	0-35mph	1.842	1.319	1.670
	36-50mph	2.611	1.814	2.348
	51+mph	3.311	2.213	2.949
LTVs:
		Anti-lock	Non-Anti-lock	Combined
Wet Pavement
	0-35mph	2.570	3.710	2.946
	36-50mph	3.654	5.637	4.309
	51+mph	4.670	7.886	5.731
Dry Pavement
	0-35mph	2.044	1.483	1.859
	36-50mph	2.896	2.040	2.613
	51+mph	3.555	2.488	3.203

Table V-16
Weighted Average Reductions In Delta-V
from Improved Tire Inflation Pressure
Alternative 3

		Anti-lock	Non-Anti-lock	Combined
Passenger Cars
Wet Pavement
	0-35mph	2.858	3.342	3.018
	36-50mph	4.065	5.092	4.404
	51+mph	5.196	7.151	5.841
Dry Pavement
	0-35mph	2.263	1.319	1.952
	36-50mph	3.208	1.814	2.748
	51+mph	4.068	2.213	3.456
LTVs:
		Anti-lock	Non-Anti-lock	Combined
Wet Pavement
	0-35mph	3.185	3.710	3.358
	36-50mph	4.530	5.637	4.895
	51+mph	5.789	7.886	6.481
Dry Pavement
	0-35mph	2.533	1.483	2.187
	36-50mph	3.589	2.040	3.078
	51+mph	4.406	2.488	3.773

Table V-17
Weighted Average Reductions In Delta-V
from Improved Tire Inflation Pressure
Alternative 4

		Anti-lock	Non-Anti-lock	Combined
Passenger Cars
Wet Pavement
	0-35mph	2.370	3.454	2.728
	36-50mph	3.371	5.263	3.996
	51+mph	4.310	7.391	5.327
Dry Pavement
	0-35mph	1.877	1.364	1.708
	36-50mph	2.660	1.875	2.401
	51+mph	3.374	2.287	3.015
LTVs:
		Anti-lock	Non-Anti-lock	Combined
Wet Pavement
	0-35mph	2.622	3.906	3.046
	36-50mph	3.728	5.935	4.457
	51+mph	4.765	8.302	5.932
Dry Pavement
	0-35mph	2.085	1.562	1.912
	36-50mph	2.954	2.147	2.688
	51+mph	3.627	2.620	3.294

Calculation of Safety Benefits

Safety benefits were calculated by reducing the delta-V for each injury by the appropriate level for each specific target population category shown in Tables V-14, V-15, V-16 and V-17.  The injury totals for each delta-V category were redistributed according to the injury probabilities of the reduced delta-V level.  This resulted in a new injury profile.  Totals for each injury severity category were then compared to the original injury totals to produce the net benefits from reducing delta-Vs.  An example of the original target population distribution and the revised distribution is shown in Tables V-18 and V-19.   Note that the revised distribution shown in Table V-19 represents a whole number delta-V change (in this case, 5 delta-V).  Since actual average reductions were fractional, interpolation was used to calculate the results of the fractional reductions.  These interpolated results are reflected in Table V-20.  Table V-21 summarizes the results for all scenarios for passenger cars under Alternative 1a.

By comparing current tire pressure levels to placard, benefit estimates reflect raising pressure levels to the placard level and retaining them there.  However, over time tire pressure will drop back down to the threshold notification level again and drivers will again fill their tires to the placard level.  Over time, the benefit that drivers obtain will be an average of the benefits from the various levels above the notification threshold.  For this analysis, it was assumed that pressure loss is roughly constant at one psi per month and a revised average psi level was calculated for passenger cars and LTVs under each Alternative.  These averages were previously shown in Table V-1.  Under the assumption that there is a reasonable correspondence between changes in delta-V and safety benefits, changes in Delta-V were recalculated based on the averages in Table V-1.  This was done by substituting the new average psi levels for the placard pressure in previous calculations.  An additional adjustment was made to reflect the impact on that portion of the fleet for which at least one tire was below the notification threshold, but for which the average psi across all 4 tires fell above the revised average psi level but below the placard level. This was done because these cases would be excluded by calculations based on psi levels below placard.  The output from this process was a set of factors that were used to modify the results.  These factors typically reduced benefit calculations based on full placard inflation levels by 50-75%.  The results of applying these factors are shown in Table V-21. 

Adjustments to Non-Preventable Crash Safety Benefits

A number of adjustments must be made to the benefit estimates in Table V-19.  These include:

1. Adjustment for crash braking distance distribution

2. Adjustment for portion of vehicle fleet with no under-inflation or under-inflation less than notification level

3. Adjustment for driver response

4. Adjustment for target population overlap travel speeds would be about 11 percent of those based on maximum impact for passenger cars, and 10 percent for LTVs.

5. Adjustment for braking threshold

6. Adjustment for current compliance.

Table V-18
Passenger Cars, Original Injury Distribution
>51 MPH Speed Limit, Wet Pavement

Delta-V	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
1	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0
3	0	0	0	0	0	0	0	0
4	280	59	2	2	0	0	0	345
5	69	20	1	1	0	0	0	91
6	359	134	5	4	1	0	1	503
7	921	433	18	12	1	0	1	1387
8	4158	2414	101	74	7	0	7	6761
9	3762	2618	132	79	0	7	7	6611
10	1113	922	51	28	2	2	2	2121
11	3889	3800	226	121	8	8	8	8068
12	1372	1555	105	50	6	0	6	3097
13	3015	3953	290	149	7	7	15	7444
14	551	826	68	33	3	1	3	1486
15	731	1242	119	52	4	2	6	2156
16	528	1006	111	44	5	2	5	1702
17	1169	2494	314	120	12	8	12	4129
18	0	0	0	0	0	0	0	0
19	141	369	61	22	2	1	3	600
20	81	231	44	15	2	1	2	376
21	265	824	181	61	7	4	8	1351
22	161	544	139	45	5	4	6	905
23	7	25	7	2	0	0	0	42
24	1	2	1	0	0	0	0	4
25	17	68	27	8	1	1	1	123
26	39	162	75	23	2	2	4	307
27	30	131	71	22	2	2	4	262
28	2	7	4	1	0	0	0	15
29	51	232	170	53	6	5	11	529
30	0	0	0	0	0	0	0	0
ETC.
Total	22717	24126	2446	1088	96	72	149	50726

Table V-19
Passenger Cars, Modified Injury Distribution
>51 MPH Speed Limit, Wet Pavement

Delta-V	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal	Total
-5	0	0	0	0	0	0	0	0
-4	0	0	0	0	0	0	0	0
-3	0	0	0	0	0	0	0	0
-2	345	0	0	0	0	0	0	345
-1	91	0	0	0	0	0	0	91
0	503	0	0	0	0	0	0	503
1	1326	49	6	4	1	0	0	1387
2	6153	541	27	27	0	7	0	6761
3	5705	826	33	33	0	7	0	6611
4	1724	365	15	15	0	2	0	2121
5	6156	1767	73	56	0	0	8	8068
6	2208	824	31	25	3	0	3	3097
7	4943	2323	97	67	7	0	7	7444
8	914	531	22	16	1	0	1	1486
9	1227	854	43	26	0	2	2	2156
10	894	740	41	22	2	2	2	1702
11	1990	1945	116	62	4	4	4	4129
12	0	0	0	0	0	0	0	0
13	243	319	23	12	1	1	1	600
14	140	209	17	8	1	0	1	376
15	458	778	74	32	3	1	4	1351
16	281	535	59	24	3	1	3	905
17	12	26	3	1	0	0	0	42
18	1	3	0	0	0	0	0	4
19	29	75	12	5	0	0	1	123
20	66	188	36	13	1	1	2	307
21	51	160	35	12	1	1	2	262
22	3	9	2	1	0	0	0	15
23	86	311	92	30	3	2	5	529
24	0	0	0	0	0	0	0	0
25	3	13	5	2	0	0	0	23
26	8	32	15	5	0	0	1	61
27	0	0	0	0	0	0	0	0
Etc.
Total	35561	13478	976	538	39	38	61	50726
Difference	12844	-10648	-1470	-550	-58	-34	-88	0

Table V-20
Estimated Passenger Car Stopping Distance Impacts
Alternative 1 (a), Unadjusted

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	14926	-12296	-1806	-629	-79	-21	-120
36-50mph	15794	-12269	-2422	-830	-100	-37	-150
51+mph	8361	-6885	-992	-365	-35	-25	-71
DRY
0-35mph	21999	-17500	-3090	-1043	-118	-69	-176
36-50mph	35882	-28661	-5004	-1627	-243	-50	-348
51+mph	12714	-7974	-3151	-1084	-137	-97	-324
Total	109676	-85585	-16465	-5579	-712	-297	-1189

Braking Distance Distribution 

Table V-20 represents safety impacts that would occur from the reduced stopping distance of a tire at the point where it would stop if pressure were corrected.  It represents the maximum change in delta-V that would occur in cases where the actual braking distance in the crash just equals the correct stopping distance.  In reality, crashes occur over a variety of braking distances, and the change in delta-V is a direct function of this distance.  This relationship is illustrated in Figure V-2 below.  The change in delta-V is virtually non-existent in crashes where braking distance is minimal, but becomes significant as the distance traveled during braking increases.

Figure V-2
Generalized Relationship Between Change in
Delta-V and Traveling Distance

To account for the variety of possible outcomes, a factor was calculated based on the relationship between calculated delta-V changes and travel distance.  The techniques used to calculate this factor are fully described in Appendix A.  The results indicate that the impacts over the variety of travel speeds would be about 7 percent of those based on maximum impact for both passenger cars and for LTV’s. 

Properly Inflated Vehicles

As previously mentioned, 26 percent of all vehicles have no tires under-inflated.  In addition, many vehicles have a level of under-inflation that would not trigger a warning from the TPMS. The target population used in the above calculations assumes a full fleet of under-inflated vehicles and must be adjusted for the portion of the fleet that is not under-inflated, and that will be notified of the problem.  The portions differ by Alternative and vehicle type.  Based on NHTSA’s tire pressure survey under Alternative 1, only 36 percent of passenger cars and 40 percent of light trucks would potentially benefit from a TPMS.  Under Alternative 2, 27 percent of passenger cars with anti-lock brakes, 26 percent of passenger cars without anti-lock brakes, 21 percent of light trucks with anti-lock brakes, and 29 percent of LTVs without anti-lock brakes would potentially benefit from a TPMS.  Under Alternative 3, 26 percent of passenger cars and 29 percent of light trucks would benefit from a TPMS.

Driver Response 

Table V-19 also represents the benefits that would accrue if all drivers responded immediately to the TPMS and inflated their tires to the proper level.  Since this is unlikely to occur, an adjustment was made to represent the driver response rate, which the agency assumes is 95 percent. Alternative 1 (a) assumes manufacturers will provide interactive or continuous readouts of individual tire pressures for direct systems.  Alternative 1 (b) assumes the just a warning light will be provided with direct systems.  This was done because of uncertainty regarding the exact nature of displays that manufacturers will install under Alternative 1.  Although there is clearly a greater potential for consumer information under Alternative 1 (a), it is not clear to what extent manufacturers will take advantage of this.  Therefore, both scenarios were examined.

Overlapping Target Populations 

As previously noted separate target populations were derived for passenger cars and light trucks because the under-inflation profile is different for these vehicle types.  These populations were stratified based on the vehicle braking.  However, a comparison of the two separate injury counts to a single count done for any passenger vehicle indicated that a small amount of double counting resulted from a simple addition of the two separate braking vehicle populations.  Based on this comparison, an adjustment factor of .9685 was applied to the benefit estimates to eliminate the overlap.

Driver Response- Braking Threshold 

 When drivers are faced with potential crash circumstances, they apply their brakes at a rate that reflects both their perceptions of the need to stop and the vehicles actual response to this need.  Theoretically, braking systems should be capable of the needed response, if drivers apply it, up to a threshold at which the tires loose their friction capabilities.  On dry pavement, this would occur when tires exceed their peak coefficient of friction and start to skid rather than grip the pavement.   In this analysis, it will be assumed that during emergency braking, all potential inadequacies in braking performance, including those caused by underinflated tires, will be perceived by drivers and that they will respond by applying more pressure to the brakes to compensate.  Under these circumstances, any small impacts to stopping distance due to changes in the tire pressure that would occur prior to skidding on dry pavement would be compensated for by the driver.  However, when skidding occurs, the driver can no longer compensate for such changes.  To reflect this, CDS data from 1995-1999 was examined to determine what portion of fatalities and injuries occurred in crashes in which skidding occurred on dry surfaces. This analysis indicated that 72% of fatalities and 54% of injuries that occurred on dry pavement happened in crashes with skidding.   These factors were thus applied to all dry pavement stopping distance benefits. 

Current Compliance

About one percent of the new car fleet already has a direct monitoring system.  This portion of the fleet would not require costs or experience benefits from this rulemaking.  A total of 5 percent of the fleet has either an indirect system (4%) or a direct system (1%).  Both current systems would meet the requirements of Alternative 4.

The above 6 adjustments were accomplished by multiplying the results in Table V-20 by factors of .11, .36, .95, .9685, .72 or .54 (dry pavement only), and .99 to account for current compliance. Similar adjustments were made for each vehicle type and Alternative. Table V-21 summarizes the total adjusted non-preventable crash benefits for passenger cars under Alternative 1 (a).  Table V-22 summarizes the benefits from non-preventable crashes under Alternative 1 (a) for both passenger cars and LTVs.  Table V-23 summarizes total benefits for all crashes and vehicle types under Alternative 1 (a).  Table V-24 summarizes total safety benefits for all crashes and vehicle types under Alternative 1 (b).  Table V-25 summarizes the potential stopping distance impacts for Alternative 2, Table V-26 shows the results for Alternative 3 and Table 27 shows results for Alternative 4.  The results indicate a potential safety impact under Alternative 1 (a) of 60 fatalities eliminated and roughly 5,300 nonfatal injuries prevented or reduced in severity from improved stopping distance.  The safety impact of Alternative 1 (b) would be 56 fatalities and about 4,960 nonfatal injuries prevented. Under Alternative 2, an estimated 29 fatalities and 2,600 nonfatal injuries would be prevented or reduced in severity.  Alternative 3 would result in 39 fatalities and about 3,400 nonfatal injuries prevented.  Alternative 4 would result in 17 fatalities and 1,560 nonfatal injuries prevented.   

Table V-21
Estimated Non-Preventable Passenger Car Stopping Distance Impacts
Adjusted for Properly Inflated Vehicles,
Delta-V Distribution, 95% Response Rate, Overlap, Threshold Braking and Current Compliance
   Alternative 1 (a)

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	343	-282	-42	-15	-2	0	-3
36-50mph	362	-281	-55	-19	-2	-1	-3
51+mph	192	-158	-23	-8	-1	-1	-2
DRY
0-35mph	273	-217	-39	-13	-1	-1	-3
36-50mph	445	-356	-62	-20	-3	-1	-6
51+mph	157	-99	-68	-14	-2	-1	-5
Total	1772	-1393	-260	-88	-11	-5	-22

Table V-22
Estimated Non-Preventable Crash Stopping Distance Impacts,
All Passenger Vehicles Adjusted for Properly Inflated Vehicles,
Delta-V Distribution, 95% Response Rate, Overlap, Threshold Braking and Current Compliance
Alternative 1 (a)

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	472	-383	-61	-21	-3	-1	-4
36-50mph	585	-460	-85	-31	-3	-1	-6
51+mph	231	-185	-31	-11	-1	-1	-3
DRY
0-35mph	584	-460	-84	-29	-4	-2	-7
36-50mph	675	-525	-103	-34	-4	-2	-10
51+mph	238	-150	-58	-20	-3	-2	-8
Total	2784	-2162	-423	-146	-18	-8	-38

Table V-23
Total Estimated Stopping Distance Impacts, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, Threshold Braking, and Current Compliance
Alternative 1 (a)

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	841	-733	-93	-36	-4	-2	-6
36-50mph	891	-841	-121	-47	-5	-2	-8
51+mph	335	-299	-45	-17	-2	-1	-4
DRY
0-35mph	1129	-979	-137	-52	-6	-3	-12
36-50mph	1239	-1113	-163	-60	-7	-3	-16
51+mph	430	-383	-101	-37	-5	-3	-13
Total	4865	-4348	-661	-248	-27	-15	-60

Table V-24
Total Estimated Stopping Distance Impacts, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, Threshold Braking, and Current Compliance
Alternative 1 (b)

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	786	-686	-87	-33	-4	-2	-6
36-50mph	834	-787	-114	-44	-4	-2	-7
51+mph	313	-279	-42	-16	-2	-1	-4
DRY
0-35mph	1057	-917	-129	-49	-5	-3	-12
36-50mph	1159	-1041	-153	-56	-6	-3	-15
51+mph	402	-358	-95	-35	-4	-3	-12
Total	4551	-4068	-619	-232	-26	-14	-56

Table V-25
Total Estimated Stopping Distance Impacts, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, Threshold Braking, and Current Compliance
Alternative 2

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	437	-378	-47	-18	-2	-1	-3
36-50mph	429	-406	-60	-23	-2	-1	-4
51+mph	176	-157	-23	-9	-1	-1	-2
DRY
0-35mph	530	-461	-63	-24	-3	-1	-6
36-50mph	613	-552	-78	-29	-3	-1	-8
51+mph	206	-185	-49	-18	-2	-2	-6
Total	2391	-2140	-320	-121	-13	-7	-29

Table V-26
Total Estimated Stopping Distance Impacts, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, Threshold Braking, and Current Compliance
Alternative 3

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	545	-474	-60	-23	-2	-1	-4
36-50mph	579	-544	-78	-30	-3	-1	-5
51+mph	219	-195	-29	-11	-1	-1	-3
DRY
0-35mph	723	-626	-88	-33	-4	-2	-8
36-50mph	799	-716	-105	-38	-4	-2	-10
51+mph	277	-245	-65	-24	-3	-2	-8
Total	3142	-2800	-424	-159	-17	-10	-39

Table V-27
Total Estimated Stopping Distance Impacts, All Passenger Vehicles
Adjusted for Properly Inflated Vehicles, Delta-V Distribution, 95% Response Rate,
Overlap, Threshold Braking, and Current Compliance
Alternative 4

	MAIS0	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Fatal
WET
0-35mph	259	-224	-28	-11	-1	-1	-2
36-50mph	260	-246	-36	-14	-1	-1	-2
51+mph	104	-93	-13	-5	-1	0	-1
DRY
0-35mph	322	-280	-39	-15	-2	-1	-3
36-50mph	366	-330	-47	-17	-2	-1	-5
51+mph	124	-111	-30	-11	-1	-1	-4
Total	1435	-1284	-193	-73	-8	-4	-17

Flat tires and Blowouts

There are many factors that influence crashes of these types.  For blowouts, there is speed, tire pressure, and the load on the vehicle.  Blowouts to the front tire can cause roadway departure, or can cause a lane change resulting in a head-on crash.  Blowouts in a rear tire can cause spinning out and loss of control.  As discussed in the target population section, a target population can be estimated for tire problems, but the agency doesn’t know how many of these crashes are influenced by under-inflation. However, reducing under-inflation will be a real benefit in reducing flat tires and blowouts.  The agency’s best estimates of these effects are discussed below.

The target population is 414 fatalities and 10,275 non-fatal injuries that occur annually in light vehicles in which the cause of the crash is a flat tire/blowout.  It is difficult to determine the impacts of under-inflation.  Puncture is the most common reason for a blowout.  However, there are also many cases where a tire is punctured, loses air, and then fails later after being driven a distance under-inflated.  In these cases, where only one tire is punctured, a TPMS meeting any of the Alternatives would provide information of the low tire pressure before the tire failed.  We are assuming that under-inflation is involved in 20 percent of the cases that caused the crash.  At the same time, we realize that the influence that under-inflation has on the chances of a blowout are influenced by the properties of the tire. Thus, we believe that better tires could take care of 50 percent of this problem and are assigning this value to the tire upgrade rulemaking.  In conclusion, it is estimated that 41 fatalities (414 x .2 x .5) and 1,028 injuries are caused annually by flat tires/blowouts, where under-inflation is the cause of the flat tire/blowout.  At the same time we estimate that there are 41 fatalities and 1,028 injuries in the target population for better tires brought about by the tire upgrade rulemaking.

The agency assumes that 95 percent of drivers will fill their tires back to placard pressure when given a warning. For this situation, the agency does not believe that the steady state analysis has any impacts on the benefits.  Any tire above the warning level is not very susceptible to a flat tire, and it probably doesn’t matter whether the tire is at a placard level of 30 psi or at a steady state level of say 27 psi in terms of its likelihood of failing due to a flat tire.  We also apply a .99 factor to take into account the one percent of the fleet that already has a direct measurement system. 

Thus, the benefits for flat tires/blowouts for Alternatives 1 through 3 are the same:

Non-fatal Injuries are divided into the AIS levels based on the injury levels in 1995-98 NASS-CDS distribution of injuries in vehicles with flat tires causing the crash.  These are:  AIS 1 = 80.1 percent, AIS 2 = 14.4 percent, AIS 3 = 3.5 percent, AIS 4 = 1.5 percent, AIS 5 = 0.5 percent.  For Alternative 4, an assumption was made that 50 percent of the flat tires could be identified by a single very underinflated tire, which the indirect system could detect.  The other 50 percent would be influenced by the fewer warnings provided by the indirect system, which when weighted by the direct and indirect system used for Alternative 4 resulted in an estimated 82.4 percent of the benefits from the other alternatives.  Thus, the benefits for Alternative 4 are 32 lives saved (39 x .824) and 797 injuries reduced (967 x .824).   

 Total Quantifiable Safety Benefits 

Table V-28 provides the total quantifiable safety benefits by alternative adding together the benefits for skidding/loss of control, stopping distance, and flat tires/blowouts.

Table V-28
Quantifiable Safety Benefit Impacts

	PDO	MAIS 1	MAIS 2	MAIS 3	MAIS 4	MAIS 5	Non-Fatal Total	Fatal
Alt 1a
Skid	-9,994	-3,725	-415	-177	-17	-11	-4,345	-46
Stop	n.q.	-4,348	-661	-248	-27	-15	-5,299	-60
Flat	n.q.	-775	-139	-34	-14	-5	-967	-39
Total	-9,994	-8,848	-1,215	-459	-58	-31	-10,611	-145
Alt 1b
Skid	-9,994	-3,725	-415	-177	-17	-11	-4,345	-46
Stop	n.q.	-4,068	-619	-232	-26	-14	-4,959	-56
Flat	n.q.	-775	-139	-34	-14	-5	-967	-39
Total	-9,994	-8,568	-1,173	-443	-57	-30	-10,271	-141
Alt. 2
Skid	-9,104	-3,394	-378	-161	-15	-10	-3,958	-42
Stop	n.q.	-2,140	-320	-121	-13	-7	-2,601	-29
Flat	n.q.	-775	-139	-34	-14	-5	-967	-39
Total	-9,104	-6,309	-837	-316	-42	-22	-7,526	-110
Alt. 3
Skid	-9,994	-3,727	-415	-177	-17	-11	-4,345	-46
Stop	n.q.	-2,800	-424	-159	-17	-10	-3,410	-39
Flat	n.q.	-775	-139	-34	-14	-5	-967	-39
Total	-9,994	-7,302	-978	-370	-48	-26	-8,722	-124
Alt. 4
Skid	6,478	2,415	269	115	11	7	2,817	30
Stop	n.q.	1,284	193	73	8	4	1,562	17
Flat	n.q.	638	115	28	12	4	797	32
Total	6,478	4,337	577	216	31	15	5,176	79

n.q. = not quantified

Fuel Economy Benefits

Correct tire pressure will improve a vehicles’ fuel economy.  Current radial tires are a vast improvement over the old-fashioned bias-ply tires, yet they still use more fuel when they are run under-inflated, although not as much as bias-ply tires.  According to a 1978 report^[1], fuel efficiency is reduced by one percent (1%) for every 3.3 pounds per square inch (psi).  More recent data provided by Goodyear indicates that fuel efficiency is reduced by one percent for every 2.96 psi, fairly close to the 1978 estimate. 

For this analysis, we assumed that there was no effect of tire over-inflation, and that savings only started once the warning went on.  In other words, if the placard pressure were 30 psi, and a warning were given under Alternative 1 at 24 psi (20 percent below placard), no benefits are assumed for those vehicles that have tires with lowest pressure above 24 psi.   For the Alternatives, data from the tire pressure survey was used to estimate the average under-inflation of all 4 tires for those vehicles for which a warning would be given.  Table V-29 provides the average under-inflation and the percentage of the fleet that would get a warning by the TPMS by alternative. 

Table V-29
Analysis of Fleet Tire Pressure Survey

	Passenger Cars Average psi below placard of those vehicles warned	Percent of Fleet Affected	Light Trucks Average psi below placard of those vehicles warned	Percent of Fleet Affected
Alternative 1a & 1b	6.1 psi	36%	7.7 psi	40%
Alternatives 2 & 3 Direct Measurement System, and Alternative 3 Hybrid Measurement System	6.8 psi	26%	8.7 psi	29%
Alternative 2 Indirect Measurement  or Hybrid Measurement System	4.9 psi	27%	6.1 psi	21%
Alternative 4 Direct and Indirect Measurement System	4.99	11%	6.33	8%

Tables V-30 and V-31 show the weighted vehicle miles traveled by age of vehicle for passenger cars and light trucks.  They also show the 7 percent discount rate and the assumed price of gasoline.  The projected price of gasoline was taken from a DOE projection from January 2001^[2]. It excludes fuel taxes, at $0.38 per gallon, since these are a transfer payment and not a cost to society.  Year 1 for these gasoline prices is estimated to be 2004, when the TPMS requirements will be in place.  The projections are for gasoline prices to steadily decline from 2001 through about 2005 when they will level off.  A second group of adjustments were made to the price of gasoline to account for environmental costs and international oil market costs. 

One product of the combustion of hydrocarbon fuels, such as gasoline and diesel, is CO₂.    The environmental and economic consequences of these releases are not included in the price of gasoline.  While there are estimates of these consequences in the literature, the administration has not taken a position on their costs.  Using estimates from the literature would result in very little savings on a per vehicle basis and they have not been included in this analysis. 

A second environmental cost of gasoline use relates to the hydrocarbon and toxic chemical releases from the gasoline supply chain, including oil exploration, refining, and distribution. Marginal costs of these activities combined have been estimated at $0.02 per gallon.^[3]

The Organization of Petroleum Exporting Countries (OPEC) operates as a cartel that restricts the supply of oil to escalate the price above the free-market level.  The greater the consumption of oil, the higher will be the price.  Since the higher price of oil applies to all oil imports from OPEC, not just the increased oil use, the financial cost to the United States exceeds the market payment for the increased amount.  Leiby et al.,^[4] estimated this impact to be $3.00 per barrel. 

This equates to $0.07 per gallon ($3/42 gallons per barrel).  The impact is dependent upon the amount of oil saved.  The $0.07 per gallon is about right for the savings of this program.

Thus, the price of gasoline has been reduced by $0.38 per gallon to account for taxes, and has been increased by $0.09 per gallon to account for environmental and economic considerations. 

Table V-30
Passenger Cars Vehicle Miles Traveled, Discount Factor, and
Assumed Price of Gasoline in (2001 Dollars)
Passenger Cars

Vehicle Age (years)	Vehicle Miles Traveled	Survival Probability	Weighted Vehicle Miles Traveled	Gasoline Price, Excluding Taxes	7 Percent Mid-Year Discount Factor
1	13,533	0.995	13,465.3	$1.05	0.9667
2	12,989	0.988	12,833.1	1.04	0.9035
3	12,466	0.978	12,191.7	1.05	0.8444
4	11,964	0.962	11,509.4	1.06	0.7891
5	11,482	0.938	10,770.1	1.07	0.7375
6	11,020	0.908	10,006.2	1.07	0.6893
7	10,577	0.87	9,202.0	1.08	0.6442
8	10,151	0.825	8,374.6	1.07	0.602
9	9,742	0.775	7,550.1	1.07	0.5626
10	9,350	0.721	6,741.4	1.06	0.5258
11	8,974	0.644	5,779.3	1.06	0.4914
12	8,613	0.541	4,659.6	1.06	0.4593
13	8,266	0.445	3,678.4	1.05	0.4292
14	7,933	0.358	2,840.0	1.05	0.4012
15	7,614	0.285	2,170.0	1.05	0.3749
16	7,308	0.223	1,629.7	1.05	0.3504
17	7,014	0.174	1,220.4	1.05	0.3275
18	6,731	0.134	902.0	1.05	0.326
19	6,460	0.103	665.4	1.04	0.286
20	6,200	0.079	489.8	1.04	0.2673
			126,678

Table V-31
Light Trucks Vehicle Miles Traveled, Discount Factor, and
Assumed Price of Gasoline in (2001 Dollars)
Light Trucks

Vehicle Age (years)	Vehicle Miles Traveled	Survival Probability	Weighted Vehicle Miles Traveled	Gasoline Price, Excluding Taxes	7 Percent Mid-Year Discount Factor
1	12,885	0.998	12,859	$1.05	0.9667
2	12,469	0.995	12,407	1.04	0.9035
3	12,067	0.989	11,934	1.05	0.8444
4	11,678	0.980	11,444	1.06	0.7891
5	11,302	0.967	10,929	1.07	0.7375
6	10,938	0.949	10,380	1.07	0.6893
7	10,585	0.924	9,781	1.08	0.6442
8	10,244	0.894	9,158	1.07	0.602
9	9,914	0.857	8,496	1.07	0.5626
10	9,594	0.816	7,829	1.06	0.5258
11	9,285	0.795	7,382	1.06	0.4914
12	8,985	0.734	6,595	1.06	0.4593
13	8,696	0.669	5,818	1.05	0.4292
14	8,415	0.604	5,083	1.05	0.4012
15	8,144	0.539	4,390	1.05	0.3749
16	7,882	0.476	3,752	1.05	0.3504
17	7,628	0.418	3,189	1.05	0.3275
18	7,382	0.364	2,687	1.05	0.326
19	7,144	0.315	2,250	1.04	0.286
20	6,913	0.217	1,500	1.04	0.2673
21	6,691	0.232	1,552	1.04	0.2498
22	6,475	0.196	1,269	1.04	0.2335
23	6,266	0.169	1,059	1.04	0.2182
24	6,064	0.143	867	1.04	0.2039
25	5,869	0.121	710	1.03	0.1906
			153,319

The baseline miles-per-gallon figure for cars was 27.5 mpg at placard inflation, and for light trucks was 20.7 mpg at placard inflation.  A sample calculation for passenger cars for Alternative 1(a) is:

The average of all four tires on a passenger car that would be warned based on our survey would be 6.1 psi lower than placard.  The average steady state condition after TPMS are in place would be 2.5 psi lower than placard.  Thus, the incremental steady state improvement of the TPMS is 3.6 psi.  Since 1 percent fuel efficiency is equivalent to 2.96 psi lower, the average passenger car with a warning would get 1.21622 percent (3.6/2.96) higher fuel economy when reinflated.  With a baseline of 27.5 mpg, the average fuel economy of those vehicles warned that increased their tire pressure up to placard would be 27.5 * 1.0121622 = 27.8345 mpg.  Based on our estimated vehicle miles traveled by age, scrappage by age, a 7 percent present value discount rate and estimated fuel costs per year, the baseline passenger car (at 27.5 mpg discounted by 15 percent to account for real on-road mileage) would spend $3,968.88 present value for fuel over its lifetime.  Those drivers warned who filled up to placard pressure and achieved 27.8345 mpg  (discounted by 15 percent to account for real on-road mileage) would spend $3,921.19 for fuel over their car’s lifetime.  The difference is $47.69.  Since 36 percent of the fleet get a warning, and it is assumed that 95 percent of the drivers would fill their tires to placard, the average benefit is $16.31 ($47.69*0.36*0.95). The estimated benefit for each subgroup under the different alternatives is shown in Table V-32. 

Table V-32
Fuel Economy Benefits Compared to the Baseline Fleet
Present Discounted Value over Lifetime
(2001 Dollars)

	Passenger Cars	Light Trucks
Alternative 1 (a)	$16.31	$35.40
Alternative 1 (b)	$14.07	$31.03
Alternative 2 & 3  Direct Measurement System	$10.16	$23.03
Alternative 2 Indirect Measurement or Hybrid Measurement System (1-3 tires)	$4.11	$6.65
Alternative 3 Indirect Measurement or Hybrid Measurement System (1-4 tires)	$10.16	$23.03
Alternative 4 Direct Measurement System	$1.24	$4.22
Alternative 4 Indirect Measurement System	$1.06	$2.74

Weighting the Alternative 2 fuel economy benefit by the percent of the fleet with ABS-based systems (67 percent) and direct measurement systems (33 percent) results in an estimated $6.11 for passenger cars and  $12.06 for light trucks.  Alternative 3 fuel economy benefits are the same for direct and indirect systems at an estimated $10.16 for passenger cars and  $23.03 for light trucks.  Weighting the Alternative 4 fuel economy benefit by the percent of the fleet with ABS-based systems (67 percent) and direct measurement systems (33 percent) results in an estimated $1.12 for passenger cars and $3.23 for light trucks.  Weighting light trucks (50 percent) and passenger cars (50 percent) and taking into account the one percent of the fleet that already has a direct measurement system and four percent of the fleet that already has an indirect measurement system results in the following overall benefit in fuel economy shown in Table V-33.

Table V-33
Fuel Economy Benefits Compared to the Baseline Fleet
Present Discounted Value over Lifetime
(2001 Dollars)

	Average Passenger Vehicle
Alternative 1 (a)	$25.88
Alternative 1 (b)	$22.32
Alternative 2	$8.99
Alternative 3	$16.43
Alternative 4	$2.06

Emissions Effect

Since there are fuel economy improvements, there are comparable savings in gasoline usage.  Fewer gallons of gasoline used mean fewer emissions.   Table V-34 shows the lifetime gallons of gasoline saved per vehicle for the different Alternatives.  These per vehicle estimates are multiplied by 16 million vehicles.  Assuming constant vehicle sales from year to year, once all vehicles in the fleet meet the standard, the annual gasoline savings are equal to the lifetime savings of fuel of one model year.   The rule of thumb for equating gasoline savings to emissions savings used by the Department of Energy is that for every billion gallons of gasoline saved, emissions are reduced by 2.4 million metric tons carbon equivalent (MMTCE).

Table V-34
Lifetime Gallons of Gasoline Saved Per Vehicle

	Passenger Cars	Light Trucks	Average Savings Per Light Vehicle
Alternative 1 (a)	22	53	38
Alternative 1 (b)	19	46	33
Alternative 2	5	10	8
Alternative 3	14	34	24

Table V-35
Annual Emission Reduction for the Fleet

	Average Gasoline Savings Per Light Vehicle	Annual Gasoline Savings (Millions of Gallons)	Annual Emissions Reduction (MMTCE)
Alternative 1 (a)	38	608	1.46
Alternative 1 (b)	33	528	1.27
Alternative 2	8	128	0.31
Alternative 3	24	384	0.92

Tread Life

Driving at lower inflation pressure impacts the rate of tread wear on tires.  This will cause tires to wear out earlier than necessary and decrease tread life.  When a tire is under-inflated, it puts more pressure on the shoulders of the tire and does not wear correctly.  This analysis will attempt to quantify the impact of increased tread wear on consumer costs. 

Based on data provided by Goodyear (see Docket No. NHTSA-2000-8572-26), the average tread life of tires is 45,000 miles and the average cost is $61 per tire (in 2001 dollars).

For Alternative 1 (a)

Assuming a direct measurement system, the TPMS warns the driver anytime a tire is 20 percent or more below the placard and the driver inflates all of the tires back to the placard levels, then we can estimate the impact on tread life using the following calculations.

Goodyear provided data estimating that the average tread wear dropped to 68 percent of the original tread wear if tire pressure dropped from 35 psi to 17 psi.  Goodyear also assumed that this relationship was linear. Thus, for every 1 psi drop in inflation pressure, tread wear would decrease by 1.78 percent [(100-68%)/(35-17psi)].  These effects would take place over the lifetime of the tire.  In other words, if the tire remained under-inflated by 1 psi over its lifetime, the tread wear would decrease by 1.78 percent or about 800 miles (45,000*0.178). 

Data from our tire pressure survey indicated that 2,136 out of 5,967 passenger car tires (36 percent) had at least one tire under-inflated by 20 percent or more below the placard level.  The average under-inflation of the 4 tires for these vehicles was 6.1 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 1 (a) would improve by 3.6 psi.   Thus, on average, passenger cars lose an estimated 2,880 miles (3.6 * 800 miles) of tread life for each tire due to the way they are currently under-inflated that could be remedied under Alternative 1(a) if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 2,736 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 47,736 miles with a TPMS.  The agency estimates that the average lifetime per passenger car is 126,678 miles. Thus, currently the average car would have 3 sets of tires on their car over its lifetime (new, at 45,000 miles, and at 90,000 miles) and with TPMS the average car would have 3 sets of tires purchased (new, at 47,736 miles, and at 95,472 miles).  The benefit to consumers is the delay in purchasing those tires and getting interest on that money at an assumed 7 percent rate of return. Using a mid-year 7 percent discount rate, the discounted present value of these delayed tire purchases is estimated to be $10.23 for those passenger cars that would be notified by a TPMS that they are under-inflated.  Since 36 percent would be notified, the present discounted benefits are $3.68 ($10.23 * 0.36) and 985 miles (2,736 * 0.36) of tread life.

For light trucks, data from our tire pressure survey indicated that 1,564 of 3,950 light truck tires (40 percent) had at least one tire under-inflated by 20 percent or more compared to the placard.  The average under-inflation of the 4 tires for these vehicles was 7.7 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 1 (a) would improve by 4.8 psi.  Thus, on average, light trucks lose an estimated 3,840 miles (4.8*800) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS. If we assume that 95 percent of the people actually inflate their tires properly, then on average 3,648 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 48,648 miles with a TPMS.  The agency estimates that the average lifetime per light truck is 153,706 miles.  Thus, the average light truck would have 4 sets of tires on their truck over its lifetime (new, at 45,000 miles, at 90,000 miles, and at 135,000 miles) and with a TPMS the average light truck would have four sets purchased (new, at 48,648 miles, at 97,296, and at 145,944 miles).  Using the same methodology as for passenger car tires, the benefit in delaying purchasing tires is estimated to be a present discounted benefit of $30.73.  Since in 40 percent of the vehicles at least one tire is under-inflated by 20 percent or more, the average benefit for light trucks is estimated to be $12.29 ($30.73 * 0.40) and 1,459 miles (3,648 * 0.40) of tread life. 

The weighted tread life savings for passenger cars and light trucks after considering current compliance for Alternative 1a is $7.91 ($3.68*.5 + $12.29*.5)*.99.

For Alternative 1 (b)

Data from our tire pressure survey indicated that 2,136 out of 5,967 passenger car tires (36 percent) had at least one tire under-inflated by 20 percent or more below the placard level.  The average under-inflation of the 4 tires for these vehicles was 6.1 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 1 (b) would improve by 3.1 psi.   Thus, on average, passenger cars lose an estimated 2,480 miles (3.1 * 800 miles) of tread life for each tire due to the way they are currently under-inflated that could be remedied under Alternative 1(b) if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 2,356 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 47,356 miles with a TPMS.  The agency estimates that the average lifetime per passenger car is 126,678 miles.  Thus, currently the average car would have 3 sets of tires on their car over its lifetime (new, at 45,000 miles, and at 90,000 miles) and with TPMS the average car would have 3 sets of tires purchased (new, at 47,356 miles, and at 94,712 miles).  The benefit to consumers is the delay in purchasing those tires and getting interest on that money at an assumed 7 percent rate of return.  Using a mid-year 7 percent discount rate, the discounted present value of these delayed tire purchases is estimated to be $8.85 for those passenger cars that would be notified by a TPMS that they are under-inflated.  Since 36 percent would be notified, the present discounted benefits are $3.19 ($8.85 * 0.36) and 848 miles (2,356 * 0.36) of tread life.

For light trucks, data from our tire pressure survey indicated that 1,564 of 3,950 light truck tires (40 percent) had at least one tire under-inflated by 20 percent or more compared to the placard.  The average under-inflation of the 4 tires for these vehicles was 7.7 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 1 (b) would improve by 4.2 psi.  Thus, on average, light trucks lose an estimated 3,360 miles (4.2*800) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 3,192 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 48,192 miles with a TPMS.  The agency estimates that the average lifetime per light truck is 153,706 miles.  Thus, the average light truck would have 4 sets of tires on their truck over its lifetime (new, at 45,000 miles, at 90,000 miles, and at 135,000 miles) and with a TPMS the average light truck would have four sets purchased (new, at 48,192 miles, at 96,384, and at 144,576 miles).  Using the same methodology as for passenger car tires, the benefit in delaying purchasing tires is estimated to be a present discounted benefit of $26.86.  Since in 40 percent of the vehicles at least one tire is under-inflated by 20 percent or more, the average benefit for light trucks is estimated to be $10.74 ($26.86 * 0.40) and 1,277 miles (3,192 * 0.40) of tread life. 

The weighted tread life savings for passenger cars and light trucks after considering current compliance for Alternative 1b is $6.90 ($3.19*.5 + $10.74*.5)*.99.

For Alternative 2

We have to consider both ABS-based vehicles and non-ABS-based vehicles since they are represented by a different group of vehicles in the tire pressure survey.  For Alternative 2, we assume that two-thirds (67%) of the vehicles would have ABS-based indirect measurement systems and one-third of the vehicles (33%) would have a direct measurement system.  For the ABS-based vehicles we assume the TPMS warns the driver anytime there is a 25 percent or more psi differential between tires.  For the non-ABS-based vehicles, we assume a direct measurement system will provide a driver warning anytime one or more tires is 25 percent or more below placard.  If we assume the driver inflates all of the tires back to the placard levels, then we can estimate the impact on tread life using the following calculations.

For direct measurement systems

Data from our tire pressure survey indicated that 1,575 out of 5,967 passenger car tires (26 percent) had at least one tire under-inflated by 25 percent or more below the placard level.  The average under-inflation of the 4 tires for these vehicles was 6.8 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 2 with direct systems would improve by 3.1 psi.  Thus, on average, passenger cars lose an estimated 2,480 miles (3.1 * 800 miles) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 2,356 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 47,356 miles with a TPMS.  The agency estimates that the average lifetime per passenger car is 126,678 miles.  Thus, currently the average car would have 3 sets of tires on their car over its lifetime (new, at 45,000 miles, and at 90,000 miles) and with TPMS the average car would have 3 sets of tires purchased (new, at 47,356 miles, and at 94,712 miles). The benefit to consumers is the delay in purchasing those tires and getting interest on that money at an assumed 7 percent rate of return.  Using a mid-year 7 percent discount rate, the discounted present value of these delayed tire purchases is estimated to be $8.85 for those passenger cars that would be notified by a TPMS that they are under-inflated.  Since 26 percent would be notified, the present discounted benefits are $2.30 ($8.85 * .26) and 612 miles (2,356 * 0.26) of tread life.

For light trucks, data from our tire pressure survey indicated that 1,148 of 3,950 light truck tires (29 percent) had at least one tire under-inflated by 25 percent or more compared to the placard.  The average under-inflation of the 4 tires for these vehicles was 8.7 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 2 with direct systems would improve by 4.3 psi.  Thus, on average, light trucks lose an estimated 3,440 miles (4.3*800) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 3,268 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 48,268 miles with a TPMS.  The agency estimates that the average lifetime per light truck is 153,706 miles.  Thus, the average light truck would have 4 sets of tires on their truck over its lifetime (new, at 45,000 miles, at 90,000 miles, and at 135,000 miles) and with a TPMS the average light truck would have four sets purchased (new, at 48,268 miles, at 96,536, and at 144,804 miles).  Using the same methodology as for passenger car tires, the benefit in delaying purchasing tires is estimated to be a present discounted benefit of $27.53.  Since in 29 percent of the vehicles at least one tire is under-inflated by 25 percent or more, the average benefit for light trucks is estimated to be $7.98 ($27.53 * 0.29) and 948 miles (3,268 * 0.29) of tread life. 

For ABS-based systems

Data from our tire pressure survey indicated that 1,622 out of 5,967 passenger car tires (27 percent) had a 25 percent or more tire pressure differential.  The average under-inflation of the 4 tires for these vehicles was 4.9 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 2 with ABS-based systems would improve by 1.2 psi.  Thus, on average, passenger cars lose an estimated 960 miles (1.2 * 800 miles) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly, then on average 912 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 45,912 miles with a TPMS.  The agency estimates that the average lifetime per passenger car is 126,678 miles.  Thus, currently the average car would have 3 sets of tires on their car over its lifetime (new, at 45,000 miles, and at 90,000 miles) and with TPMS the average car would have 3 sets of tires purchased (new, at 45,912 miles, and at 91,824 miles). The benefit to consumers is the delay in purchasing those tires and getting interest on that money at an assumed 7 percent rate of return.  Using a mid-year 7 percent discount rate, the discounted present value of these delayed tire purchases is estimated to be $3.50 for those passenger cars that would be notified by a TPMS that they are under-inflated.  Since 27 percent would be notified, the present discounted benefits are $0.95 ($3.50 * 0.27) and 246 miles (912 * 0.27) of tread life.

For light trucks, data from our tire pressure survey indicated that 831 of 3,950 light truck tires (21 percent) had a 25 percent or more tire pressure differential.  The average under-inflation of the 4 tires for these vehicles was 6.1 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 2 with ABS-based systems would improve by 1.7 psi.  Thus, on average, light trucks lose an estimated 1,360 miles (1.7*800) of tread life for each tire due to the way they are currently under-inflated that could be remedied if everyone filled all their tires back up to the placard pressure when they were notified by a TPMS.  If we assume that 95 percent of the people actually inflate their tires properly (some of them might only fill some tires and not all of their tires), then on average 1,292 miles of tread life would be saved per tire. 

If the average current lifetime of tires is 45,000 miles at current inflation levels, the average lifetime could be 46,292 miles with a TPMS.  The agency estimates that the average lifetime per light truck is 153,706 miles.  Thus, the average light truck would have 4 sets of tires on their truck over its lifetime (new, at 45,000 miles, at 90,000 miles, and at 135,000 miles) and with a TPMS the average light truck would have four sets purchased (new, at 46,292 miles, at 92,584, and at 138,876 miles).  Using the same methodology as for passenger car tires, the benefit in delaying purchasing tires is estimated to be a present discounted benefit of $10.85.  Since in 21 percent of the vehicles there is a tire pressure differential of 25 percent or more, the average benefit for light trucks is estimated to be $2.28 ($10.85 * 0.21) and 271 miles (1,292 * 0.21) of tread life. 

The weighted tread life savings for passenger cars and light trucks after considering current compliance for Alternative 2 is $2.76 ($3.68*.5 + $12.29*.5)*.99.

For Alternative 3

For direct measurement systems and for ABS-based system

The analysis for Alternative 3 for direct measurement systems and for ABS-based systems is the same as the analysis for Alternative 2 for direct systems.

In summary, assuming that half of the vehicle sales in the future are passenger cars and half of the sales are light trucks, the average present discounted value benefit for tread wear savings for Alternative 1 (a) is $7.99 ([$3.68 + $12.29]/2) and 1,222 miles ([985 + 1,459]/2) of tread life per tire.  For Alternative 1(b) the average is $6.97 ([$3.19 + $10.74]/2) and 1,063 miles ([848 + 1,277]/2) of tread life per tire.

For Alternative 2 and 3 direct measurement system, the average benefit for tread wear savings is $5.14 ([$2.30 + $7.98]/2) and 780 miles ([612 + 948]/2) of tread life per tire.  For Alternative 2 ABS-based measurement system, the average benefit for tread wear savings is $1.62 ([$0.95 + $2.28]/2) and 259 miles ([246 + 271]/2) of tread life per tire.  Assuming that 33 percent of the fleet uses the direct measurement system and 67 percent of the fleet has ABS, the average present discounted value benefit for tread wear for Alternative 2 is $2.79 ($5.14*0.33 + $1.62*.67) and 431 miles (780*.33 + 259*.67) of tread life per tire.  

For Alternative 3, the average benefit for tread wear savings for the ABS-based measurement system is the same as for the Alternative 3 direct system.  Thus, the benefits for Alternative 3 are $5.14 and 780 miles of tread life per tire.    

For Alternative 4

Similar calculations as above were performed for Alternative 4.  For passenger cars, the average under-inflation of the 4 tires for these vehicles was 4.99 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 4 would improve by 4.5 psi.  Thus, the incremental improvement is .49 psi for passenger cars, which results in a savings of $1.44 and 63 miles. For light trucks, the average under-inflation of the 4 tires for these vehicles was 6.33 psi.  Based on our steady state assumptions discussed earlier, the average psi of the fleet under Alternative 4 would improve by 5.2 psi.  Thus, the incremental improvement is .49 psi for light trucks, which results in a savings of $7.22 and 112 miles for light trucks.  The savings for passenger cars for the direct system is 20 percent and for the indirect system is 17 percent.  The savings for light trucks for the direct system is 20 percent and for the indirect system is 13 percent.  Combining and weighting those direct and indirect systems results in a savings of $0.26 and 12 miles for passenger cars and $1.11 and 17 miles for light trucks.    Combining these into an average fleet and multiplying that result by 95 percent current compliance results in the overall average of $0.65 in fuel savings and 15 miles. 

Table V-36 shows the tread life savings per vehicle after considering current compliance.
Table V-36
Estimated Tread Life Savings per Vehicle
(Weighted Passenger Cars and Light Trucks)

	Savings per Vehicle
Alternative 1 (a)	$7.91
Alternative 1 (b)	$6.90
Alternative 2	$2.76
Alternative 3	$5.09
Alternative 4	$0.65

There are other potential non-quantified benefits of increasing tread wear.  Some people would not have to purchase the last set of tires for a vehicle if they were going to scrap the vehicle soon, or if it were totaled in a crash shortly before they were going to purchase new tires.  So, there will be cases where the total purchase price of tires $244 ($61 per tire * 4) will be saved.  However, we can’t estimate the frequency of that occurrence. 

Non-quantifiable Benefits

Under-inflation affects many different types of crashes. These include crashes which result from:

1. an increase in stopping distance,
2. flat tires and blowouts
3. skidding and/or a loss of control of the vehicle in a curve, like an off-ramp maneuver coming off of a highway at high speed, or simply taking a curve at high speed
4. skidding and/or loss of control of the vehicle in a lane change maneuver,
5. hydroplaning on a wet surface, which can affect both stopping distance and skidding and/or loss of  control. 
6. overloading the vehicle

The agency has quantified the effects of under-inflation in a crash involving skidding and loss of control, flat tires and blowouts, and the reduction in stopping distance.  However, it cannot quantify the effects of under-inflation hydroplaning, and overloading the vehicles.  The primary reason that the agency can’t quantify these benefits is the lack of crash data indicating tire pressure and how large of a problem these conditions represent by themselves, or how often they are contributing factors to a crash.  The agency does not yet collect tire pressure in its crash data investigations. 

Skidding and/or loss of control from hydroplaning

The conditions that influence hydroplaning include speed, tire design, tread depth, water depth on the road, load on the tires, and inflation pressure.  At low speeds (less than about 50 mph), if your tires are under-inflated, you actually have more tire touching the road.  However, hydroplaning does not occur very often at speeds below 50 mph, unless there is deep water (usually standing water) on the road.  As you get to about 55 mph and the water pressure going under the tire increases, an under-inflated tire has less pressure in it pushing down on the road and you have less tire-to-road contact than a properly inflated tire as the center portion of the tread gets lifted out of contact with the road.  As speed increases to 70 mph and above and water depth increases due to a severe local storm with poor drainage, the under-inflated tire could lose 40 percent of the tire-to-road contact area compared to a properly inflated tire.  The higher the speed (above 50 mph) and the more under-inflated the tire is, then the lower the tire-to-road contact and the higher is the chance of hydroplaning.  

Tread depth has a substantial impact on the probability of hydroplaning.  If you make a simplifying assumption that the water depth exceeds the capability of the tread design to remove water (which most likely would occur with very worn tires), then an approximation of the speed at which hydroplaning can occur can be estimated by the following formula: 

Hydroplaning speed  = 10.35 x inflation pressure^[5]

Under this assumption of water depth exceeding the capability of the tread design to remove water:

This is presented to show the relative effect of inflation pressure on the possibility of hydroplaning. 

Overloading the vehicle

When a vehicle is overloaded, (too much weight is added for the suspension, axle, and tire systems to carry) and the tires are under-inflated, there is an increased risk of tire failures.  This can result in a loss of control of the vehicle.  

Property Damage and Travel Delay

TPMS will impact safety by reducing both the incidence and severity of crashes.  When crashes are prevented, the property damage and travel delay that would have occurred are prevented as well.  In a 1996 report^[6], NHTSA estimated that property damage costs averaged over $3000 per crash and travel delay averaged $260 per crash ($1994).  These savings would accrue to crashes prevented by TPMS.  However, most benefits from TPMS would accrue from crashes that still occur but with a reduced severity.  It is unclear what the impact would be on travel delay and property damage from these reductions.

Potential Benefits for Antilock Brake Systems

If a manufacturer decided that the difference in the cost between an indirect and direct TPMS was enough to make antilock brakes a marketable feature for that vehicle, then it might decide to increase its use of ABS and use an indirect TPMS to meet the phase-in part of the final rule. The agency has been analyzing the safety impacts of ABS for several years.  The initial findings^[7]were mixed.  Fatal crash involvements in multi-vehicle crashes on wet roads and fatal crashes with pedestrians and bicyclists were significantly reduced. However, these reductions were offset by a statistically significant increase in the frequency of single vehicle, run-off-road crashes (rollovers or impacts with fixed objects).   The run-off-road crashes were surprising in view of the good performance of ABS in stopping tests conducted by the agency and others. The agency has spent several years trying to determine why run-off-road crashes have increased with ABS, without a satisfactory answer. 

Two more recent studies of ABS have found no statistically significant fatality improvement with ABS.  The Farmer study from IIHS^[8] found the results shown in Table V-37.  (A ratio of 1.0 means there is no effect on fatalities.  Less than one is a reduction in fatalities, more than 1.0 is an increase in fatalities.  In order for the results to be statistically significant, the confidence bounds would have to be both below 1.0 or both above 1.0).   The only statistically significant findings were that fatalities went up in non-GM cars in calendar years 1986-1995 and overall from 1986-1998.

Table V-37
Results from the Farmer Study of the Impacts of ABS

	All crashes	95 percent confidence bounds
	Ratio	Lower	Upper
GM cars in 1993-95	1.03	.94	1.12
GM cars in 1996-98	.96	.87	1.05
GM cars in 1993-98	.99	.93	1.05
Non-GM cars in 1986-95	1.16 (Significant)	1.06	1.27
Non-GM cars in 1996-98	.91	.77	1.06
Non-GM cars in 1986-98	1.09 (Significant)	1.01	1.18

Farmer’s theory is that people learned how to use ABS better in calendar years 1996-98 and they were no longer overinvolved in run off the road fatal crashes.  Farmer never states that ABS reduced fatalities.  His statement on the GM cars for 1996-98 is "When all fatal crash involvements were considered, disregarding in which vehicle the fatalities occurred, the risk ratio was slightly lower than, but not significantly different from 1.0."  

The second recent analysis by Ellen Hertz (NHTSA)^[9], in which she included optional ABS to get more cases, also resulted in no overall statistically significant findings for fatalities.  ABS effects were examined separately for passenger cars and light trucks for five types of crashes (frontal impacts, side impacts, rollover, run-off-road, and pedestrian).  The only statistically significant finding was that fatalities in light truck rollover crashes went up in ABS vehicles compared to non-ABS vehicles (see Table V-38).  In this study, a negative is an improvement in safety (fewer fatalities) and a positive is an increase in fatalities. 

Table V-38
Results from the Hertz Study of the Impacts of ABS

	Point	95 percent confidence bounds
	Estimate	Lower	Upper
Frontal – PC	-4.9%	-19.9%	11.5%
Frontal – LTV	17.9	-7.1	49.6
Side Impact – PC	32.4	-1.0	77.2
Side Impact – LTV	-0.3	-42.3	72.2
Rollover – PC	12.3	-17.2	52.2
Rollover – LTV	106.5 (Significant)	49.2	185.9
Run-Off-Road – PC	-13.4	-28.1	4.2
Run-Off-Road – LTV	21.8	-12.6	69.5
Pedestrian – PC	-0.4	-16.3	18.4
Pedestrian – LTV	-22.7	-50.1	19.6

The Hertz study did find that antilock brakes had an overall effect of reducing crashes, but not fatalities. 

If NHTSA believed that antilock brakes were cost/beneficial, we would consider requiring them to be installed.  We have not considered requiring antilock brakes because we have not been able to show that they are beneficial in reducing fatalities.  Reducing their costs, by offsetting the costs with a TPMS, does not affect our conclusions to date that we have not been able to prove that ABS reduces fatalities. 

^[1] Evaluation of Techniques for Reducing In-use Automotive Fuel Consumption; The Aerospace Corporation, June 1978.  Original reference from Goodyear, pp 3-45.

^[2] DOE Energy Information Administration, Annual Energy Outlook 2001, Table A3, Energy Prices by Sector. 

^[3] "Effectiveness and Impact of Corporate Average Fuel Economy (CAFE) Standards", National Research Council, July 2001, Pages 5-5 to 5-6. 

^[4] "Oil Imports: An Assessment of Benefits and Costs", P.N. Leiby, D.W. Jones, T.R. Curlee, and L. Russell, 1997, ORNL-6851, Oak Ridge National Laboratory, Oak Ridge, Tenn. 

^[5] "Mechanics of Pneumatic Tires" edited by Samuel K. Clark of the University of Michigan, published by NHTSA, printed by the Government Printing Office in 1981.

^[6] "The Economic Cost of Motor Vehicle Crashes", 1994, DOT HS 808 425, NHTSA, July 1996.

^[7] "Preliminary Evaluation of the Effectiveness of Antilock Brake Systems for Passenger Cars", NHTSA,  December, 1994, DOT HS 808 206. 

^[8] "New Evidence Concerning Fatal Crashes by Passenger Vehicles Before and After Adding Antilock Braking System", Charles M. Farmer, Insurance Institute for Highway Safety, February, 2000.

^[9] "Analysis of the Crash Experience of Vehicles Equipped with All Wheel Antilock Braking Systems (ABS) – A Second Update Including Vehicles with Optional ABS", NHTSA, September 2000,