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

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In summary, a winch rated for a vehicle's weight and slope can pull that much when used with a ramp angle of 30 degrees.
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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?
 
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  • #2
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?
 
  • #3
Skrambles said:
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.
 
  • #4
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.
 

What is the simple formula for a winch?

The simple formula for a winch is Force = Mass x Acceleration, or F = m x a. This means that the amount of force required to lift an object with a winch is directly proportional to its mass and the acceleration at which it is being lifted.

What is the formula for calculating the ramp angle?

The formula for calculating the ramp angle is Angle = inverse tangent (height/length). This means that the angle of a ramp is determined by dividing the height of the ramp by its length and finding the inverse tangent of that value.

How do you calculate the required winch force for a specific object?

The required winch force for a specific object can be calculated using the formula F = m x a, where m is the mass of the object and a is the acceleration at which it is being lifted. This will give you the minimum amount of force needed to lift the object.

What is the relationship between the ramp angle and the force required to pull an object up the ramp?

The relationship between the ramp angle and the force required to pull an object up the ramp is that the steeper the angle of the ramp, the more force will be required to pull the object up. This is because the steeper the ramp, the greater the vertical distance the object needs to be lifted, resulting in a higher required force.

How does the mass of an object affect the angle of a ramp needed to lift it?

The mass of an object does not directly affect the angle of a ramp needed to lift it. However, a heavier object may require a steeper ramp in order to decrease the force needed to pull it up. The angle of the ramp is primarily affected by the height and length of the ramp, as well as the force required to lift the object.

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