# Falling body question

1. Sep 23, 2013

Okay guys, a different one for you. I am in the planning stages of building a structure that will simulate a motor vehicle collision. The process would be a motor vehicle will be hoisted to a specific height and then dropped. The height, and the weight of the vehicle will determine the simulated speed of the vehicle at the time it hits the "crash-pad".

What I need to know is the formula for working this out. I have the vehicles weight, the height and obviously gravity (I am not taking into account wind resistance deliberately).

If anyone is able to help me out i'd be forever in your debt. If you have an app or spreadsheet that just requires me to enter the weight of the vehicle and height and then reveals the velocity on impact I would be even happier!

Thanks in advance for any and all help.

2. Sep 23, 2013

### Staff: Mentor

I remember that you are in Emergency Medical Services and S&R. What is the purpose of this crash simulator? If it is to crumple up vehicles to make extrication exercise vehicles, then the question is pretty easy to answer using basic kinematic equations. But if the purpose is directed at some court testimony/evidence purposes, then dropping a vehicle from a height is not a good way to simulate crash damage. Any lawyer worth a darn would be able to discredit any evidence based on dropping a vehicle versus doing an at-speed horizontal collisiion with the vehicle(s).

3. Sep 23, 2013

Hi berkeman, you have an excellent memory. :-) No, the query isn't in relation to an inverstigation. Unfortunately, there is no "safer" way to simulate a motor vehicle collision on the horizontal plane - the logistics is too great and the risk does not warrant it as a viable avenue. A drop from height to simulate a motor vehicle collision and then have my motor vehicle extrication crew carry out the extrication is all I am after. :-)

4. Sep 23, 2013

### eigenperson

The speed of a falling object upon reaching the ground is $\sqrt{2gh}$, where $g$ is the acceleration due to gravity and $h$ is the height. You can derive this formula from basic kinematic considerations, or from the conservation of energy.

The weight of the vehicle doesn't matter -- remember, all objects fall at the same rate, regardless of mass.

EDIT: It just occurred to me that it is more likely that you have already decided what speed you want, and would like to determine the height to drop from, in which case the height needs to be $v^2/2g$.

5. Sep 23, 2013

Okay, so if I were to drop a vehicle from 20 meters, the equation would look something like this:

SQRT((2*9.81^2)*20)?

6. Sep 23, 2013

### Staff: Mentor

Remember to include units in all of your equations, so you don't mix up mph and m/s

7. Sep 23, 2013

Pardon my ignorance, i'm not a physics major. lol. What Units did I miss?

8. Sep 23, 2013

### eigenperson

The units of g = 9.81 are m/s2, and the units of your height are meters. So the answer will be in meters per second.

But why did you square of 9.81?

9. Sep 24, 2013

Apologies, probably an oversight on my behalf. Thanks for the correction. I looked for the error for so long it started looking right.

10. Sep 24, 2013

### SteamKing

Staff Emeritus
Now, figuring out how to hoist a car 20 m into the air before dropping it. What happens if the car doesn't hit the ground square when you drop it, i.e., it lands on its roof, for example?

Not to burst anyone's bubble, but the car companies have figured out how drive cars into fixed barriers when they crash test a model. They take pitchers and movies of the crash, too.

11. Sep 24, 2013

I completely agree SteamKing. I am neither a car manufacturer or someone who has a lot of disposable income. I merely wanted some insight into an idea that is in the PLANNING stage that would hopefully give me an idea if I was on the right track. The cheaper alternative is to build a hoist and simulate a road crash. Especially when I can place other objects underneath it and "cause" a specific collision for my extrication crews to work on.

12. Sep 24, 2013

### 256bits

Just get a bulldozer and squish the car to the desired amount to simulate a crash.
And you can simulate side impacts, roof depressions and any other imaginative twisted metal scenario you like.

I do not see why by dropping a car you expect the car to become any thing useful for you play with it may just crumple the front end of the car and the 'victim' can just open the door and walk out.
You have to consider that each car crash will not be the same ever, so if you would like like give your guys experience in extraction techniques, you would have more control of the simulated damage this way.

If you want to give your guys experience in real accidents and what cars look like afterwards then just take them out to car wreck grounds.

13. Sep 24, 2013

256 bits, some great ideas there mate. Really well thought out. Unfortunately we don't have the resources available not the cash to hire a bulldozer everytime we need to crush a car for simulation. While I agree this would be easier, we are looking for a long term solution. This idea being one of several discussed during out last planning meeting. In all fairness this is just one of six ideas that have been floated and a such needs to be explored in great detail. When we look at the height of the tower, this is probably going to be a non-viable option as we have height restrictions due to a close by airport.

An excavator and front end loader are also in the planning; however, these come with the requirement of having appropriately trained and licences personnel at the cost of thousands. As a volunteer Unit this is why we need to explore several avenues. As a road rescue instructor of several years I have seen many systems, and am just exploring options.

I acknowledge your input and thank you. :-)

14. Sep 24, 2013

### mic*

Paliadon, I would suggest constructing a steep ramp c/w a winch setup for hoisting the "victim vehicle" into position. Simillar to a really steep, oversized tilt-tray towtruck.

I suggest this because I understand how crushing a car with a bulldozer with not simulate an acute impact accurately. Plus there are greater ongoing costs associated with the dozer. However the points raised by others about the inconsist landings and other safety concerns with dropping a vehicle are valid.

Your calculations for using a ramp would not change greatly as long as the car/s used still rolls. Just work with the height of the ramp (from where the nose of the vehicle is when fulled winched up), not the length of the ramp.