By: Expert No. 43224, Ph.D., and Sylvian Poncet
This paper presents a simple relationship between a vehicle’s acceleration and the occupant’s head acceleration during low speed rear-end collisions. Only experimental data obtained from tests performed on human volunteers, is used to establish the relationship. It was found that the head acceleration, on the average, is at least two and a half times larger than vehicle’s acceleration.


Low speed, 8-16 [Km/h] (5-10 [mph]), rear-end collisions (LSREC) represent an important percentage of car accidents (7 out 1000 people will be involved in such accidents). These collisions usually do not cause any visible damage, but they may cause neck and upper back injuries. In spite of many years of research and testing, it is still difficult to determine the value of the impact force in these accidents and consequently the related injuries.

A dynamic model for LSREC, which considers the bumper as a spring/damper combination, was proposed in [1]. This assumption is based on the fact that there is very little, if at all, permanent damage to the car and therefore very little energy is absorbed during the collision. Thus, the impact can be considered as an elastic one. The model predicts the acceleration of both vehicles (bullet and target) after the collision. In [2] tests were conducted to determine whether the linear model proposed in [1] could be adapted for the simulation of low speed impacts of vehicles with various combinations of energy absorbing bumpers (EAB). The types of bumper used in these tests included, in various combinations: foam, pistons and honeycomb systems. Impact speeds varied between 4.2 and 14.4 [km/h] (2.6 and 9.0 [mph]) and 16 tests with 6 different combinations of bumpers were conducted. This study reveals that vehicle accelerations are approximately linear with impact velocity for a wide variety of bumper systems and that a linear mass-spring-damping model may be used to model these kinds of collisions.

However, the cause of injuries is the acceleration of the occupants’ heads, in particular those in target vehicle. The motion of the head due to the impact is called whiplash and is demonstrated in Figures 1.

Figure 1: Head motion in LSREC

The severity of the injuries depends of the range of motion and head acceleration. While the above model can predict the target vehicle acceleration, it is not sufficient for the prediction of the head acceleration since there is a large difference between the vehicle’s acceleration and the occupant’s head acceleration as shown in Figure 2.

Although many LSREC tests were performed using dummies and cadavers, very few were performed on volunteers, and even fewer were fully instrumented. The purpose of this note is to collect data obtained by tests performed on volunteers and to determine a relationship between the target vehicle’s and its occupant’s head accelerations.

vehicle’s accelerations Figure 2: Vehicle, shoulder, neck and head accelerations of a target vehicle’s occupant (V-Vehicle, S-Shoulder, H-N-Neck & Head).

Sources of Data

The first test on human occupant is described in [3]. In this test a 1941 Plymouth to rear-ended a 1947 Plymouth with impact velocities ranging from 11.2-36 [Km/h] (7-20[mph]). The tests used dummies and volunteers as occupants. It should be noted that these are very old vehicles and their bumpers are by far more rigid than current ones.

In [4], human volunteers were exposed to 10[mph] LSREC tests. These tests were conducted with 1981 and 1984 Ford Escorts with men and women volunteers 27 to 58 years old. It was concluded that: “In spite of the fact that human volunteers in the present study differed in sex, age, height, weight and initial spinal condition, kinematics for all occupants were similar”. Also, “head acceleration multiplication factor” was defined as the ratio of the peak head acceleration to the peak vehicle acceleration. This factor was used to evaluate cervical injury and it was determined that in cases where this ratio exceeds the value of 2, it usually indicates cervical injuries.

In [5] tests were conducted with males and females occupants 22 to 54 years old with impact speeds up to 16[Km/h] (10[mph]). Two mid 1970’s Volvos with two different head restraints were tested. Rear-end collisions tests are also reported in [6] where two 1979 Plymouth where used. In these tests the impact speeds ranging from 1.8- 11.6[Km/h] (1.1-7.2 [mph]).

The results of rear-end collisions with higher impact speeds, 48 [Km/h] (30 [mph]), are reported in [7]. The test vehicles in this case were two standard Audi 80s. The use of this data is limited since the speed was too high to be considered as low speed. However, the data will be presented here for comparison purpose.

Experimental Data Compilation

The experimental results were grouped according to Impact speed and it is shown in Figure 3. It is clear that for high speed impact, higher than 40[Km/h], the occupant’s head acceleration is almost constant and independent of the vehicle acceleration. These cases are not considered to be low speed impact since large plastic deformations are involved. The data for the mid-range speeds, 10-20[Km/h], are not conclusive. However, the data for the low speed, 0-10[Km/h], experiments show a trend which need exploration.

Vehicle Acceleration Figure 3: Vehicle and head accelerations for different impact speeds.

The data related to slow speed impact (0- 10[km/h]) are redrawn in Figure 4 and a simple linear regression of the data yielded:

Ah = 2.75(Av −0.33) (1)

Ah – Head acceleration in g’s
Av – Vehicle acceleration in g’s

with a correlation index of R2 = 0.80.

Linear regression for low speed data Figure 4: Linear regression for the low speed data.

Since the repeatability of these experiments is relatively low, due to difficulty in controlling all the experimental parameters, the high value of the correlation index (R2=0.8) indicates that the approximation given in Eq. 1 is valid.


Low speed rear end collisions happen very frequently. In most cases there is no or very minor damage to the vehicles and as a result, it is assumed no injury occurred. However, in some cases occupants do complain about neck and back pain which is characterized as “whiplash” injury. The reason for this pain is the exposure of the head to high acceleration.

Experimental results from low speed rear end collisions, involving human subjects, show that the peak head acceleration is at least two and a half times larger than peak acceleration of the struck vehicle. This assessment is correct for impact speed below 10 [km/h] (6.8[mph]). However, it should be realized that the volunteers, who participated in these tests, were aware and anticipated the impact, and therefore “prepared” themselves. In reality, the occupants do not anticipate the impact and therefore their heads’ acceleration might be even higher.

This “amplification” of the vehicle’s acceleration explains why injuries are reported although no vehicle damage was observed.

Expert No. 43224 is a mechanical engineer in Boca Raton, FL. He is experienced in vehicle accident reconstruction, low speed impact, product liability (ladders, chairs, elevators, hydraulic lifts, power tools, machinery etc.), slip, trip, and fall, building and safety codes violations (stairs, rails, etc.).

Sylvian Poncet is a third year student at IFMA (French Institute of Advanced Mechanics) in the Advanced Production Systems Department, where he interned for companies including AREVA and AMG located in France. This work was performed during his internship at the Mechanical Engineering Department at Florida Atlantic University.


  1. 1. Ojalvo, I. U., Cohen, E. C., “An Efficient Model for Low Speed Impact of Vehicles”, SAE 970779 and SP-1226, pp.193-199.
  2. 2. Ojalvo I.O., Weber B. E., D. A. Evenson, T. J. Szabo, J. B. Welcher, “Low-Speed Car Impacts With Different Bumper Systems: Correlation of Analytical Model With Tests”, SAE Technical paper 980365, 1998.
  3. 3. D.M. Severy, J.H. Mathewson and C.O. Bechtol, M.D., “Controlled automobile rear- end collisions, an investigation of related engineering and medical phenomena”, Can Serv Med J. 1955,11(10):727-59.
  4. 4. T.J. Szabo and J.B. Welcher, “Human subject kinematics and electro myographic activity during low speed rear impacts”, SAE Technical paper 962432, 1996.
  5. 5. T.J. Szabo, J.B. Welcher, R.D. Anderson, M.M. Rice, J.F. Ward, L.R.Paulo, and N.J. Carpenter, “Human occupant kinematic response to low speed rear-end impacts”, SAE Technical paper 940532, 1994.
  6. 6. D. H. West, P.E; J.P. Gough, P.E; G.T.K. Harper, P.E., “Low speed rear-end collision testing using human subjects”, Accident Reconstruction Journal, May/June 1993.
  7. 7. R. Wagner,”A 30mph front/rear crash with human test persons”, SAE Technical paper 791030, 1979.
  8. 8. G.P. Siegmund, D.J. King, and J.M. Lawrence, “Head/Neck kinematic response of human subjects in low-speed rear-end collisions”, SAE Technical paper 973341, 1997.

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Acceleration, Accident Reconstruction, Accident Investigation, Back Pain, Collision, Kinematics, Neck Pain