Example Data Table
| Input |
Example Value |
Result Guide |
| Struck vehicle mass |
1500 kg |
Passenger car estimate |
| Striking vehicle mass |
1800 kg |
Larger car or light SUV |
| Speeds |
0 and 40 km/h |
Closing speed is 40 km/h |
| Restitution |
0.20 |
Mostly plastic impact |
| Contact time and crush |
0.12 s and 0.45 m |
Average force is near 89.532 kN |
| Peak factor |
1.80 |
Peak force is near 161.157 kN |
Formula Used
The calculator uses a straight line rear collision model.
Final speed of struck vehicle:
v1 = [m1 - e m2]u1 / [m1 + m2] + [(1 + e)m2u2] / [m1 + m2]
Final speed of striking vehicle:
v2 = [m2 - e m1]u2 / [m1 + m2] + [(1 + e)m1u1] / [m1 + m2]
Impulse: J = m1 × (v1 - u1)
Average force by time: Ft = |J| / t
Delta V energy: E = 0.5 × m1 × (Delta V)²
Average force by distance: Fs = E / s
Peak force estimate: Fpeak = Favg × peak factor
Average acceleration: a = Favg / m1
How to Use This Calculator
- Enter the mass of the struck vehicle.
- Enter the mass of the rear striking vehicle.
- Select the speed unit for both vehicles.
- Enter both initial speeds before impact.
- Add a restitution value between zero and one.
- Enter contact time and effective crush distance.
- Choose the force method for the final result.
- Press Calculate to view the result above the form.
- Use CSV or PDF buttons to save the report.
Rear Impact Force Calculation Overview
Rear impact force describes the average load transferred during a rear collision. The value depends on mass, speed change, contact time, crush distance, and restitution. A small change in contact time can strongly change force. A short pulse creates a high average load. A longer pulse spreads the same impulse over more time.
Why This Calculator Helps
Rear impacts are complex events. Real crashes involve bumper geometry, seat stiffness, tire grip, frame crush, braking, and road slope. This calculator gives a controlled physics estimate. It uses momentum, impulse, and work energy ideas. It is useful for study, comparison, training, and early engineering review. It should not replace a certified crash reconstruction report.
Inputs That Matter
Vehicle mass sets how much momentum changes. Striking vehicle speed and struck vehicle speed define closing speed. Restitution describes how bouncy the impact is. A value near zero means a plastic collision. A higher value means more rebound. Contact time supports an impulse based force. Crush distance supports an energy based force. The peak factor converts average force into a simple peak estimate.
Reading The Results
The calculator reports final speeds for both vehicles. It also reports delta V for the struck vehicle. Delta V is often more useful than impact speed alone. The average force by time comes from impulse divided by contact time. The average force by distance comes from energy divided by crush distance. The selected force follows the method chosen in the form. Peak force is only an estimate.
Practical Use
Use measured data when available. Enter realistic masses with passengers and cargo. Use consistent speed units. Keep restitution between zero and one. Use a longer contact time for softer structures. Use a shorter distance for stiff structures. Compare several cases instead of trusting one entry. This helps show sensitivity.
Limits And Safety
This tool is educational. It cannot see hidden damage, occupant posture, seatback motion, or medical injury risk. Real investigations need photographs, event data, skid evidence, crush measurements, and expert judgment. Use the result as a physics guide only. Record every assumption beside the output. Save separate reports for soft, normal, and stiff cases. This makes later review easier and clearer for teams too.
FAQs
What is rear impact force?
Rear impact force is the estimated load applied to a struck vehicle during a rear collision. It can be estimated from impulse, contact time, speed change, or crush distance.
Is impact speed the same as delta V?
No. Impact speed is the closing speed before collision. Delta V is the struck vehicle speed change caused by the collision. Delta V often gives a better physics view.
What does restitution mean?
Restitution describes rebound. Zero means a fully plastic collision. One means a perfectly elastic collision. Real vehicle impacts usually stay much closer to the plastic side.
Which force method should I use?
Use the time method when contact duration is reliable. Use the distance method when crush distance is reliable. Use combined mode for a balanced early estimate.
Why is peak force higher than average force?
Collision force is not constant. It rises and falls during the crash pulse. The peak factor estimates the highest force from the average force.
Can this calculator predict injury?
No. Injury depends on many factors. Seat design, posture, head restraint position, age, health, and impact pulse shape all matter. This tool only estimates physics values.
What units should I use for mass?
Use kilograms for vehicle mass and occupant mass. The calculator converts common speed, distance, and time units internally before solving the equations.
Can I use this for legal reports?
This page is for education and early review. Legal, insurance, or safety decisions should use certified crash reconstruction methods and qualified expert analysis.