Correlation between a car's horsepower and maximum strength of Cable

[primesource20]

Science quiz question:

How to determine the correlation between a car’s horsepower / torque and the maximum break strength of a cable that will hold the motor stationery.

Assuming that the wheels of a car do not spin, how can I determine what the required cable’s break strength needs to be to ensure that a car can be held stationery . My objective is to find the correlation between the torque or horsepower of any vehicle and the corresponding break strength of cable that will hold the car in check.

 

[russ_watters]

Any manual transmission car can spin its wheels so this is a function of tire static friction force only. Engine has nothing to do with it.

 

[primesource20]

This is a theoretical question therefore I need to assume that the tires do not spin. I want to determine the strength of cable required to restrain the power of the motor.

 

[Fish4Fun]

Assuming safety is a factor, I would use 4 times the vehicle's weight. Static friction is a function of the normal force, and unless there is some reason to assume a very high Us (>1), using 4x vehicle weight should give you a good safety margin. If safety is not a concern, and you really want to watch a car break free, try using a cable equal to the vehicle's weight.

Fish

 

[Fish4Fun]

This is a theoretical question therefore I need to assume that the tires do not spin. I want to determine the strength of cable required to restrain the power of the motor.

The answer is really almost infinite.

Power = Work/Time = (Force * Distance)/Time

If you decrease the distance and increase the time then Force goes through the roof! That is, if you move the cable 1 foot per hour @ 100HP the force is:

100HP * 33,000ftlbf/min * 60min/hour * 1/ft => 198,000,000lbsf

You might achieve this through gearing or anyone of a number of schemes.

Fish

 

[Lsos]

In fact you don't need a car. Even a human on a bicycle could break any thickness of cable given a suitable transmission.

 

[russ_watters]

Assuming safety is a factor, I would use 4 times the vehicle's weight. Static friction is a function of the normal force, and unless there is some reason to assume a very high Us (>1), using 4x vehicle weight should give you a good safety margin. If safety is not a concern, and you really want to watch a car break free, try using a cable equal to the vehicle's weight.

Fish

Just for clarity, 4x the weight makes for a 400% safety factor.

 

[Jobrag]

I don't know how strong the cable needs to be but a few years ago on Top Gear a tug-of-war team held and then pulled backwards a top of the range Mercedes with Jeremy Clarkson trying to pull the team.

 

[jack action]

As said earlier, it has nothing to do with engine power. It depends on http://hpwizard.com/tire-friction-coefficient.html" .

 

[K^2]

Assuming safety is a factor, I would use 4 times the vehicle's weight. Static friction is a function of the normal force, and unless there is some reason to assume a very high Us (>1), using 4x vehicle weight should give you a good safety margin.

That's a good starting point. I'd go with 2x weight, honestly, but if you feel like giving yourself extra room. Anyways, you still need to do some math.

The value above gives you maximum force on the wheel, which you can convert to maximum possible torque on wheels. Engine doesn't spin wheels directly, though. There is a gear box in between, which can significantly alter the torque. In high gear, torque on engine is significantly higher than on wheels. So you have to multiply by gearing ratio of highest gear to get torque on engine.

Now, you compare this value to the peak torque of the engine. Odds are, the torque of the engine is going to be lower. In either case, take the lower of two values, add a bit of safety margin, and that's the torque you have to deal with.

Finally, the torque needs to be converted back into tension. Find the greatest arm length between the engine's shaft and attachment points, multiply that by torque, and that should give you the minimum breaking strength you should be shooting for.