Would a 2400 lb SRC survive a head on collision with an 8400 lb SUV ?

The following analysis shows why the occupants of the SRC would survive.

An SUV weighing 8400 lb travels West at 50 mph and collides with a 2400 lb SRC headed East at 50 mph.

Using conservation of momentum we can say that the momentum headed west before and after the collision will be the same. We can use this fact to calculate the velocity of the SRC and SUV after the collision.

Before : M1V1 + M2V2 = 8400*50 + 2400(-50) = 50 * (8400-2400) = 300,000

After : M1V1 + M2V2 = 300,000 = (8400+2400) * V2

We solve for V2 = 300,000 /(8400+2400) = 27.8 mph

Before the collision the two cars were headed in opposite directions. After collision they are both headed West but at the reduced speed of 27.8 mph.

This assumes the smaller SRC has an impact absorbing nose which absorbs and dissipates, but does not store, the energy of collision.

The change in SRC velocity is 50 + 27.8 = 77.8 mph.

Now we can look at the speed , G level and duration of the collision.

Would the SRC driver survive ?

Convert mph to feet per second : 77.8 * 5280/3600 = 114.1 fps

Assume a constant G level during the collision of 34 G where 1 G = 1 gravitational acceleration of 32 feet per second per second.

Now we can calculate the time to decelerate : since velocity V = acceleration A times time T

T = V/A = 114.1 FPS / (34G x 32 fpss) = .105 seconds or 105 milli-seconds.

The distance traveled is found using D = 1/2 * A * T * T :

(1/2) * (34 * 32) * (.105 * .105) = 5.98 feet

So we need a crash cushion about six feet long to keep the G level down to 34 G.

Next we calculate the severity index : G to the 2.5 power * T

(34 to the 2.5) * .105 = 707

Since the severity index is below 1000 the SRC meets FMVSS 208 .

This Federal Motor Vehicle Safety Standard covers occupant safety in motor vehicle collisions.

The driver would survive.

FMVSS 208 stipulates that a motor vehicle hit an unyielding barrier at 35 mph and that the G levels, as measured at a test dummies head, should not exceed the severity index of 1000.

This standard assumes collisions at 35 mph, or less, with vehicles of equal mass or less. Obviously this standard is unrealistic and inadequate. Maybe that is why 30,000 Americans die in car accidents each year.

The above analysis assumes a constant G level. A changing G level would be more realistic.

The plot below is for a 2400 lb SERC at 45 mph colliding with an 8400 lb SUV at 45 mph

I ran a differential equation with a non uniform G level and got the following outputs :

6 foot crash cushion that deflects 60 inches or 5 feet,

max G level of 50

SRC velocity changes from 45 forward to 25 mph backwards for a total of 70 mph

and severity index of 759

Again the SRC driver and passenger would survive.