How Much Force is Applied to a Spotlight at 100 MPH?

[00529174]

Hello, I am a cop and I have a problem that we are unable to find an answer for at the station.

We want to put portable spotlights on the roofs of our cars. We want to know at 100 MPH how many pounds of force are being applied to the the front of the spotlight. We need to know this so we can buy the appropriate magnets to ensure the spotlights don't blow off.

For the life of me I cannot find the answer to this. Can anyone help?

Thanks!

 

[Mike706]

It would be necessary to specify the specific lights you are referring to (or at the very least, the shape and dimensions). Also, if you don't find your answer here, you may get a larger response in the mechanical engineering or aerospace engineering forums.

edit:
Also, in case you don't know, when you do find out how much force would be on the lights, that isn't the force you will need for the magnets (henceforth f). There are two cases you would need to watch out for: the light sliding off the roof; the light tipping over and flying off the roof.

Sliding:
You would need to know the coefficient of static friction (henceforth u), or at least an estimate of it. You could then find the maximum force that could be applied to the light before sliding occurred (henceforth F) as: F = f * u. You would then compare F to the force on the lights from wind resistance, and ensure that F is larger. You will probably want it to be several times larger to have a factor of safety, especially since there will be guesswork involved.

Tipping:
If - viewed from the side of the car - the light is much shorter (vertically) than it's base is wide, this probably won't be much of an issue. If not, it could definitely become important. You would then need to know information about the moments (basically, how the air is torquing the light). Placement of the magnet(s) would also be important when trying to see if it would tip. This is a more complicated analysis than for sliding.

 

[Dale]

The formula for drag is:
$$F_D=\frac{1}{2} \rho v^2 C_D A$$

In your problem the density of air, ρ, depends on temperature. At 0°C it is about 1.3 kg/m^3. I would probably use that number unless you are in an area where it gets significantly colder than that for prolonged periods. You already gave v, which is 100 mph or 45 m/s.

So that leaves the cross-sectional area, A, and the drag coefficient $C_D$, both of which depend on the shape of the housing of the searchlight. You can easily measure the cross sectional area yourself. The drag coefficient is much more difficult to measure, but it typically ranges from .4 to 1.2 for objects which are not specifically designed to be streamlined. I would just estimate it as 2 to give yourself a margin of safety.

 

[Andre]

Check the drag equation here.

you'd only need to figure out the drag coefficient, that would probably be around one.

A is the area in square meters,
v is the speed in meter per seconds, for 100mph should be 44.4 m/s
rho density of air is temperature dependent around 1.2 kg/m-3

Notice that the force is in Newton or kgm/sec-2 and has to be converted to pounds

Would that help?

 

[Mike706]

The formula for drag is:
$$F_D=\frac{1}{2} \rho v^2 C_D A$$
.

The problem I see with this is that formula assumes that the light is the complete shape, and there is nothing else solid nearby. Unless the centroid of the light's cross-section is much higher than the roof of the car, there's a good chance that formula is going to be inaccurate due to the (much larger) car's effect on the surrounding air.

Edit:
To the original poster: What I mean is that the formula is probably not going to be accurate unless the majority of the light's cross-sectional area (viewed from the front of the car) is much higher than the roof of the car. Basically it would have to have a base with negligible cross-sectional area. Whatever was elevating the light (a rod, bar, etc) would also have to have negligible cross-sectional area.

(This is obviously not desirable since it will make it easier for the light to tip over, btw)

 

[Danger]

The simple answer is: rivets.

 

[Mike706]

The simple answer is: rivets.

Agreed. Another solution would just be to get in touch with the manufacturer - I'm sure they have done all this testing already.

 

[Danger]

Agreed. Another solution would just be to get in touch with the manufacturer - I'm sure they have done all this testing already.

That is assuming that their lights are intended for vehicular use. He only said that they're spotlights, not what type they are. If they happen to be Q-Beams with a hand grip, a special housing would have to be devised for them. (I know because I did it.)

 

[Mike706]

That is assuming that their lights are intended for vehicular use. He only said that they're spotlights, not what type they are. If they happen to be Q-Beams with a hand grip, a special housing would have to be devised for them. (I know because I did it.)

This actually makes a lot more sense than what I was thinking. If this is the case, and the light is not intended to be mounted on a vehicle, I see at least these options for allowing it to be detachable:

- Make some sort of fixture that the light can be quickly snapped into, and permanently attach said fixture to the roof.

- Come up with rough calculation using above formula. Take one light, and sacrifice it for testing. Assuming the force is still proportional to the velocity squared, when the car is moving 130 mph the light will have about 1.7 times the drag force as it will at 100 mph. If it holds at this speed, your magnet is probably fine. If not, increase the strength of the magnet until it holds securely at 130mph+. If the light can have multiple orientations, be sure to test it in multiple orientations. Once you have the right setup, test out the first few at 130 mph; if there are no issues with these 5, go all out.

 

[Danger]

- Make some sort of fixture that the light can be quickly snapped into, and permanently attach said fixture to the roof.

I'm going to preface this with a statement to clarify things in case my previous claim was misinterpreted. I designed a mounting system for hand-held Q-beams, but didn't actually build it. It turned out that they're available with a trunnion mount.
Anyhow, after thinking about casting the handles into silicone and a couple of other things, I realized that the easiest thing was to just use clamps. That can be anything from professional carpentry or machinists' units down to a couple of scrap steel strips held together with bolts.

 

[256bits]

QUOTE=00529174;4016622]Hello, I am a cop and I have a problem that we are unable to find an answer for at the station.

We want to put portable spotlights on the roofs of our cars. We want to know at 100 MPH how many pounds of force are being applied to the the front of the spotlight. We need to know this so we can buy the appropriate magnets to ensure the spotlights don't blow off.

For the life of me I cannot find the answer to this. Can anyone help?

Thanks![/QUOTE]

Police officers call themselves cops - I didn't know the colloqual term was used amongst yourselves. Nonetheless...

I tend to think that a portable spotlight to be attached to a vehicle with a magnetic mount would have to come as a complete package ( would it not? ), especially that to be used by a police force. Attaching to an existing spotlight a magnet with glue or a screw just might be too ad hoc of a fixup job for security, durability, and safety. Not sure what you have in mind.

An electrical cord would supply power for the spotlight and the directional control. If the magnetic mount fails ( and it will at some point ) the cord has to be strong enough and also attached securily enough to the spotlight, so that you do not lose the spotlight at 100 mph where it then becomes a lethal projectile. In addition, all parts, including the magnet, would have to stay together so that individual pieces do not come flying off at high speed. Unless you or you know of someone who is very adept and capable of adapting an existing spotlight to a magnetic mount, you and your police force, could be looking at a legal ramification should a loose spotlight cause personal or property damage to a third party, depending of course on your jurisdiction.

 

[PhanthomJay]

For what it's worth, at 100 mph, the pressure is 25 psf (pounds per square foot) on a cylindrical surface , and about 40 psf on a flat surface. Assuming your spotlight and support is 1 square foot in exposed frontal area, that's only about 40 pounds of force. Use a safety factor and call it 100 pounds . Beyond that, there are other factors to consider, like overturning or rounding a sharp curve.

 

[Lsos]

I imagine dynamic forces (from cornering/ braking) would be as (if not more) strong as aerodynamic forces.

Also, 100 mph seems slow. Surely the cars can (and do) go faster. That, plus what happens if you run into a gust of wind? That can add directly to the other forces causing 100 mph to easily become 130 mph...and drag rises as a squared function of speed.