What's the simple formula for winch/ramp/angle?

[prefetch]

i'm not a physics guy, or a mechanical engineer, but i think this should be a really simple formula - I'm assuming some of you folks will know this off the top of your head:

okay, so I'm trying to figure out how big of a winch to buy for a very large tow truck i am building. winches are rated based on how much they can pull. eg. a 20,000 lb winch can pull 20,000 lbs at a 0 degree incline (flat surface.)

so if i have a vehicle that weighs 40,000 lbs, and a ramp angle of 30 degrees, and a drag coefficient of .5 (if I'm towing a disabled tracked vehicle, I'm guessing a drag coefficient as high as .5 isn't unreasonable) then how big of a winch would i need to pull this up the ramp?

i'm looking for a formula, so i can change the values of my variables: weight of vehicle, drag coefficient of vehicle, winch size, angle of ramp.

is this a basic formula that you folks know?

 

[Skrambles]

You would need a winch that can pull more than:

(40,000 lbs.) * sine(30 degrees) + (0.5) * (40,000 lbs.) * cosine (30 degrees) = ~ 37,000 lbs.

You should be careful about assuming your drag coefficient. Perhaps you could measure the force require to pull a vehicle of some known weight up a hill of some known slope?

 

[prefetch]

You would need a winch that can pull more than:

(40,000 lbs.) * sine(30 degrees) + (0.5) * (40,000 lbs.) * cosine (30 degrees) = ~ 37,000 lbs.

You should be careful about assuming your drag coefficient. Perhaps you could measure the force require to pull a vehicle of some known weight up a hill of some known slope?

cool. yeah, that's a good idea on the drag coefficient, i guess that makes a big difference. i think i have some ideas on that.

anyway, thanks a bunch! good on you.

 

[Mech_Engineer]

You also have to consider what the "disabled" vehicle might be stuck in or behind. For 4x4's it's best practice to spec a recovery winch at about double the weight of the veihicle, in case it's stuck in mud or large rocks. This helps to keep the duty cycle and strain on the winch down, in addition to giving you an extra safety factor for rare circumstances. So for a 4500lb SUV, you want your winch to be rated at about 9000lbs; for a 40,000lb tank you'll want the winch to be rated for at LEAST 40,000lbs, and I would aim closer to 80K.

Keep in mind though you can use snatch blocks (pulleys) to double or quadruple the pulling capability of whatever winch you decide on.