Kühnel (1974) conducted a series of tests using a moving dummy and three different vehicles. The 50th percentile male dummy was propelled at 6 km/h (walking speed) into the path of the test vehicle. The test vehicle impact speed ranged between 35 km/h and 60 km/h. Dummy displacement was recorded at 24 millisecond intervals using high-speed photography and head, chest and pelvis acceleration were also measured. Test vehicles included a VW Beetle, a VW van and an Opel sedan. The data, as interpreted by the author of this thesis, can be seen in Table 2.2. Of note are the timed portions of the dummy’s travel, including the sliding/tumbling portion along the ground. From these measurements the ratio of airborne travel to tumbling/sliding travel can be determined.
Although the data set is fairly complete only the horizontal displacement versus time of the dummy was recorded and it is not clear which of the maximum vertical displacement measurements (i.e. the maximum throw height, or apogee, of the pedestrian’s trajectory, measured by Kühnel using photogrammetry) relate to which test. This is unfortunate, as it makes it difficult to ascertain the proportion of the dummy’s velocity present at the moment of impact with the pavement is transferred to
of friction between the dummy and the ground ranges between 1.2 and 1.6 (averaged for the impacts involving each vehicle-type and ignoring one extraneous result from the Opel tests). These values are obviously too high. For 80% conservation of horizontal velocity between the airborne and sliding phases the coefficient of friction drops to between 0.7 and 1.0. Likewise, for 60% conservation of velocity the coefficient of friction lies between 0.4 and 0.6.
Launch angle can also be approximated from Kühnel’s data. If it is assumed that the pedestrian attains a launch velocity equal to the sum of the vectors of the vehicle’s pre-impact velocity and the pedestrian’s pre-impact velocity (which would, actually, only occur in the instance of an inelastic collision) and incorporating the pedestrian’s post-impact horizontal velocity then the average launch angle was 40º for the VW Beetle tests, 46º for the Opel tests and 42º for the VW van tests. However, if the Projectile and Sliding Equation is used to solve for launch angle the results are 6.7º, 9.4º and 6.1º for the Beetle, Opel and VW van tests, respectively. This would appear to result, at least in part, from the Projectile and Sliding Equation describing an inelastic collision where the energy transfer results. In reality both the vehicle and pedestrian are likely to undergo elastic and possibly plastic deformation during the contact phase. The transfer of energy into deformation results in reduction of pedestrian launch velocity, compared to what would be expected as a result of an inelastic collision. Consequently, for the Projectile and Sliding Equation to match the correct throw distance with a launch velocity that is too high an under prediction of launch angle is required.
The centre of mass apogee height calculated using the launch angles determined from the Projectile and Sliding Equation ranged between 1.0 and 2.6 metres with an average of 1.24 metres, assuming an initial centre of mass height of 1.0 metre1. The eight apogee measurements quoted by Kühnel average 1.20 metres, indicating at least some agreement with the results indicated by the Projectile and Sliding Equation.
However, as noted, Kühnel fails to note which apogee measurement belongs to which
1 Note: Dummy centre of mass height estimated using the 55% of height rule, based on a height in shoes of 1.8 metres. The 55% rule gives approximately the same result as the method detailed in NASA’s Man-Systems Integration Standards (MSIS) Volume 1: L (from top of head to centre of mass)
= 0.486 x height (cm) – 0.014 x weight (lbs) – 4.775, using the 50th percentile male height of 177 cm and weight of 164 lb. And yes, NASA does really mix metric and imperial units, which possibly
test. Because the Projectile and Sliding equation represents an inelastic collision with a launch velocity that is unrealistically high (and a launch angle that is unrealistically low) it would be expected that the apogee predicted by the Projectile and Sliding equation would also be too low. Further testing or a clarification of Kühnel’s measurements would be of value.
The throw distance data reported by Kühnel and comparison with the throw distance predicted by the Projectile and Sliding equation, Collins equation and Searle’s equations from his 1993 paper can be seen in the three graphs in Figures 2.10, 2.11 and 2.12. Searle’s equation and a coefficient of friction of 0.7 reasonably accurately predict the throw distances obtained from the VW Beetle and Opel sedan tests.
Searle’s vmin equation gives reasonable agreement with the results from the VW van tests when using a coefficient of friction between 0.7 and 1.0. These correlations can be seen in Figures 2.10 to 2.13.
Searle’s 1993 equation appears to offer consistently accurate results with limited influence from the value used for pedestrian-ground coefficient of friction. Searle’s vmin equation does indeed appear to offer a valid indication of minimum speed for a given throw distance. Collins’ equation tended to underestimate and may be used in place of Searle’s vmin.
The Projectile and Sliding equation appears to predict an impact speed that is too high when a 70:30 airborne:sliding ratio is used, despite this ratio being indicated in an average of Kühnel’s data for the car (VW Beetle and Opel R3) impacts. As previously noted, the pedestrian’s velocity following impact is over-predicted by the Projectile and Sliding equation and results in an over-prediction of vehicle velocity when a lower than would be expected launch angle (such as 6º) is used in conjunction with the correct airborne:sliding ratio. An increase in launch angle input, a reduction of the airborne travel proportion and/or a low pedestrian-ground coefficient of friction has to be applied for the Projectile and Sliding equation to better match the data.
Throw distance vs impact speed for Kuhnel dummy testing compared with projectile and sliding equation with 70:30
airborne:sliding ratio and 6 degree launch angle
0
Collins, coefficient of friction 1.0
Searle 93, coefficient of friction 1.0
Searle vmin 93, coefficient of friction 1.0
Searle 93, coefficient of friction 0.7
Figure 2.10 Equations matched to 70:30 airborne:sliding ratio of VW Beetle and Opel R3 assuming a 6 degree pedestrian launch angle (launch angle indication from Beetle tests)
Throw distance vs impact speed for Kuhnel dummy testing compared with projectile and sliding equation with 70:30
airborne:sliding ratio and 10 degree launch angle
0 Collins, coefficient of friction of 1.0
Searle 93, coefficient of friction of 1.0
Searle vmin 93, coefficient of friction of 1.0
Searle 93, coefficient of friction 0.7
Figure 2.11 Equations matched to 70:30 airborne:sliding ratio of VW Beetle and Opel R3 assuming a 10 degree pedestrian launch angle (launch angle indication from Opel tests)
Throw distance vs impact speed for Kuhnel dummy testing compared with projectile and sliding equation with 50:50
airborne:sliding ratio and 6 degree launch angle
0 2 4 6 8 10 12 14 16 18 20
0 5 10 15 20
Throw distance (m)
Impact speed (m/s)
VW Beetle
Opel R3
VW Van
Projectile and sliding, 0.4 coefficient of friction Projectile and sliding, 0.7 coefficient of friction Projectile and sliding, 1.0 coefficient of friction Collins, coefficient of 1.0
Searle 93, coefficient of 1.0
Searle vmin 93, coefficient of friction 1.0
Searle 93, coefficient of friction 0.7
Figure 2.12 Equations matched to 50:50 airborne:sliding ratio of VW Van tests assuming a 6 degree pedestrian launch angle
Impact
Note: = missing data where, in the instance of "Head Contact on Bonnet" the substitutions are averages, whilst for "Head Contact on ground" the substitutions are "Pelvis contact on ground"
Table 2.2 Data from Kühnel’s Experiments