Stopping Distance

Table of Contents

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 earlier 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 vehicles with ABS and without ABS. The stopping distance was collected from 45 mph to 5 mph. Goodyear found that collecting the data at 5 mph reduced the variability in the results as compared to a full stop to 0 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 examined the new data submitted by Goodyear and determined that it provided a much more comprehensive data set than was used previously for the earlier PEA. The variety of   water depths and tread depths were particularly important to resolving critical concerns with the initial data sets used in the earlier 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, 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 confirmed that tread depth has a significant influence on stopping distance. Overall, the new test data provided a comprehensive picture of the impacts of tire inflation on stopping distance, and were relatively free of the contradictions found in the earlier data sets. For these reasons, NHTSA based 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 :

p⁺_i,j = percent probability risk of MAIS j+ injuries at i mph delta-V,

x _i,j = the number of j+ injuries (i.e., MAIS 0, MAIS 1+, MAIS 2+, …, fatal) at i mph delta-V

T_i = total number of occupants at i mph delta-V

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

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

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.

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.

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:

a)     Has low tire pressure, and
b)     Would be notified by the TPMS
c)     Is driven by drivers who will respond to the warning


Data from NHTSA’s tire pressure survey (see Table III-1) indicate that 26 percent of passenger cars and 29 percent of LTVs have at least one tire that is 25 percent or more below recommended placard pressure. For these vehicles, notification of this under-inflation would not be given until the system is triggered. For example, under the proposed requirements, a direct TPMS will trigger at 25% below placard pressure, or roughly 22.5 psi for passenger cars and 26.25 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.  However, in order to experience this reduction in stopping distance, the driver must respond to the warning. For the March 2002 Final Economic Assessment, NHTSA assumed that 95 percent would respond to a warning and refill their tires back to the placard level. 

Preliminary results from a recent survey conducted to determine consumer reaction to existing TPMS systems indicated that in 95% of cases where vehicles had direct systems, the drivers responded by taking appropriate action. These preliminary survey results thus validate NHTSA’s initial assumption. However, the vehicles that have existing TPMS tend to be more expensive luxury vehicles that are typically purchased by upper income populations. Since these groups are typically more safety conscious than lower income groups, it is likely that the survey results imply a lower level of response for the overall driving public. Based on this, the overall response rate across all income groups will be estimated to be 90%.

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:

Ip_(s)=Pp*I_(s)*Pu*Pr

Where,

Ip_(s)= Preventable injuries of severity (s)

Pp = portion of crashes that are preventable

I_(s)= Existing injuries of severity (s)

Pu = portion of vehicles with under-inflated tires that will receive notification from TPMS

Pr = portion of drivers who will respond to the TPMS notification

The results of this analysis are shown for passenger cars under Compliance Options 2 and 3 in Table V-7. The results for LTVs are shown in Table V-8, and for all passenger vehicles Table V-9. Results for Compliance Option 1 will be summarized at the end of this section, but will not be demonstrated. 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, as well as potential overlap with“loss of control”crashes, which are accounted for separately in a previous section. A combined adjustment factor of .959 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, as well as current compliance. These concepts are discussed in detail in the following section on non-preventable crashes.

The benefits from preventable crashes, shown in Tables V-7, 8 and 9 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. These crashes are addressed separately in a later section of this analysis.

NOTE: Negative signs indicate reductions in injury levels.

NOTE: Negative signs indicate reductions in injury levels.

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:

SD = Vi²

Where:

SD =Stopping Distance (in feet)

Vi = initial velocity (mean speed limit for specific data group + 5 mph)

g = gravity constant (32.2 ft/second squared)

Mu = tire friction constant (ratio of friction force/vertical load)

E = ABS braking efficiency (estimated @ 0.8)

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

Mp = 0.83140+(.0037109*ip)-(0.0038408*Vi)+(0.000023292*Vi²)

Ms = 0.55093+(0.0029423*ip)-(0.0036979*Vi)-(0.000020146*Vi²)

For Dry surface conditions

Mp = 0.978764+(.002557*ip)-(0.005542*Vi)+(0.0000470863*Vi²)

Ms = 0.717073+(0.000618*ip)-(0.005242*Vi)+(0.000082917*Vi²)

Where:

Mp = Mu peak value

Ms = Mu slide value

ip = inflation pressure (psi)

V_i= initial vehicle speed (mph)

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 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 with a 215/70R15 Integrity tire, and a Ford Ranger with a P235/75R15 Wrangler tire. 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:

SD = (Vi^{2 -}Vii²)

Where:

SD = braking distance

Vi = initial speed before braking

Vii = speed to which vehicle braking is measured

 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 SDs were then compared to the actual stopping distance found in the corresponding vehicle tests. The actual SDs were weighted to reflect an average of the full and half tread tests. Weighting factors for the actual SDs 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 inch. For the Wrangler tire (assumed to represent LTVs), full tread was 13/32 inch and half tread was 6.5/32 inch). Data from the NHTSA survey indicate that about 2/3 of all vehicle tires had tread depths more similar to the½tread level and about 1/3 had tread depths more similar to the full depth levels.

A comparison of the predicted and actual weighted SDs 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-11.

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:

V(d) = velocity of vehicle at distance d after braking

Vi = initial velocity before braking

a = deceleration     

d = distance traveled during braking of vehicle

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:

a = (V(d)²-Vi²)

Since V = 0 at d, the formula becomes:

a = (Vi²)/(2*d)      (the negative sign that would precede the formula indicates deceleration 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:

a = (Vi²)

Where:

SDu = stopping distance with under-inflated tires

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:

DELTA-V = (V(d)*3600/5280)/2

Where:

DELTA-V = the change in velocity resulting from increased tire pressure.

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 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 this requirement.  The distribution of each level of under-inflation is shown in Table V-12. The left column indicates the average under-inflation of the 4-tires, given that one tire was under-inflated by 25 percent or more.

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 psi was assumed. The rates of under-inflation in Table V-12 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-13 for each passenger car and LTV target population category for vehicles with 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. 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. This analysis assumes a set point of 25 percent below the placard pressure, or 7.5 psi based on the assumption of a 30 psi recommended pressure. Benefits would only accrue to those tires that are more than 7.5 psi beneath their recommended pressure. For LTVs, benefits would accrue for those tires that are more than 8.75 psi beneath their recommended pressure.

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 Table V-13. 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-14 and V-15. Note that the revised distribution shown in Table V-15 represents a whole number delta-V change (in this case, 6 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-16. Table V-20 summarizes the results for all scenarios for passenger cars under Compliance Alternative 2.

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-1x. 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-1x. 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 4 tire average 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 to about 60% of their full placard level. 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.

5)     Adjustment for braking threshold

6)     Adjustment for current compliance.

Braking Distance Distribution

Table V-16 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.

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 26 percent of passenger cars and 29 percent of light trucks would benefit from a TPMS.

Driver Response 

Table V-16 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, based on preliminary results from a survey of TPMS equipped vehicles, the agency estimates to be 95 percent.

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. In addition, there is potential overlap between the target population examined here and the one used to calculate “out of control” crash impacts earlier in this analysis. To adjust for this overlap, an analysis of overlapping cases was conducted and an adjustment of 1% (i.e., a factor of .99 was applied) was made to reflect these cases.

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. On dry pavement, only these crashes with skidding would benefit from the TPMS. These factors were thus applied to all dry pavement stopping distance benefits. Given the high level of skidding involved on dry pavement, this analysis assumes that all crashes that occur on wet pavement involve some level of skidding and thus would benefit from TPMS. This may slightly overstate the impacts of TPMS in wet pavement crashes.  

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%). However, the indirect systems would not meet the requirements of this proposal.

The above 6 adjustments were accomplished by multiplying the results in Table V-16 by factors of .07, .26, .95, .9589, .72 or .54 (dry pavement only), and .99 to account for current compliance. Similar adjustments were made for each vehicle type and Compliance Option. Table V-17 summarizes the total adjusted non-preventable crash benefits for passenger cars under Compliance Option 2. Table V-18 summarizes the benefits from non-preventable crashes under Compliance Option 2 for LTVs. Table V-19 summarizes the non-preventable benefits for all vehicle types under Compliance Option 2. Table V-20 summarizes total safety benefits for all crashes (Preventable and Non-Preventable) for passenger cars under Option 2. Table V-21 summarizes the Total safety benefits for all crashes for LTVs under Option 2. Table V-22 summarizes the total potential stopping distance impacts for all crashes and all vehicle types under Option 2. Note that safety benefits would be identical for Compliance Options 2 and 3. Table V-23 shows the potential stopping distance impacts across all crashes and vehicles for Compliance Option 1, which assumes a continuous readout of tire pressure is provided.

The results indicate a potential safety impact under Compliance Options 2 and 3 of 40 fatalities eliminated and roughly 3,500 nonfatal injuries prevented or reduced in severity from improved stopping distance. The safety impact of Compliance Option 1 would be 43 fatalities and about 3,700 nonfatal injuries prevented

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