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Thread: How to calculate Gradeability?

  1. #1
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    How to calculate Gradeability?

    I've been frustrated trying to find an understandable formula for calculating the climbing ability in degrees for various vehicle set ups.the formulas i have found through googling are baffling and don't seem to come up with an accurate result. I know that gradeability is dependant on tractive effort the road wheels apply at the road surface, which is calculated by multiplying max net engine torque by overall gear ratio in low 1st divided by tyre radius.if i use a series 2a swb as an example.
    115lbft torque x40.6:1 gear ratio =4669lbft of torque at the axles,divide by 15''(1.25ft) tyre radius =3750lbs of tractive effort at the road surface.
    To my mind that means if the landrover was loaded to a gross vehicle mass of 3750 lbs it could theoretically drive up a vertical slope.but an old operators manual I have gives the fully loaded gradeabilty (2900lbs tare plus 800lbs load) at 45 degrees(100%).The various formulars i've found on the net come up with numbers ranging from 66% to 92%, well below 45 degrees and obviously nowhere near 90 degrees.
    If there is a technical oracle on here who can explain in simple laymans terms the proper formula, with an example to show how the result was arrived at it would be much appreciated. I am trying to work out the effect in percentage terms that different tyre sizes have on climbing ability. Also I'd like to be able to calculate the minimum axle torque is required to climb gradients of different steepness, in order to compare theoretical antisquat numbers with actual measured real world numbers of torque tube(unimog) type suspensions.
    eg, how much to climb 20degrees, 30 , 40, and so on .With a rolling resistance for dry hard surfaces to keep it simple.
    Wagoo.

  2. #2
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    I think you are overthinking it.

    A landrover in standard form should have the GEARING to drive any slope fully loaded (note that LR specify a lower GVM for offroad conditions).

    What will always be the limiting factor is traction/friction.

    To drive a 45 degree slope you need to have perfect friction. So anyone who claims to have driven up a slope 45 degree or greater that is significantly longer than the wheelbase of their vehicle (i.e. too long to use momentum to carry you over) is full of BS.

    So in short - IME traction is always the limiting factor in a standard LR, not gearing.
    Last edited by isuzurover; 6th December 2010 at 09:57 AM.

  3. #3
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    Quote Originally Posted by isuzurover View Post
    I think you are overthinking it.

    A landrover in standard form should have the GEARING to drive any slope fully loaded (note that LR specify a lower GVM for offroad conditions).

    What will always be the limiting factor is traction/friction.

    To drive a 45 degree slope you need to have perfect friction. So anyone who claims to have driven up a slope 45 degree or greater that is significantly longer than the wheelbase of their vehicle (i.e. you can't use momentul to carry you over) is full of BS.

    So in short - IME traction is always the limiting factor in a standard LR, not gearing.
    Yes Ben I know that traction will be the limiting factor, unless overloaded, a very tired engine and/or too large a tyre are part of the equation,and i've run out of power on a few occasions for all the above. but that doesn't really answer my question.There are mathematical formulas on the net for calculating climbing abilty but the way they are laid out makes them difficult to follow for this old codger. I'll give you an idea why I would like to know. Unimogs are criticised for having too much antisquat geometry in their torque tube suspension design. If I want to build a vehicle with Unimog axles and a 4ft long one link wishbone to replace the torque tube, I can calculate how much lifting force is applied via the wishbone pivot to the chassis at mid wheelbase for a given amount of axle torque. if I have a formula for calculation how much axle torque is required to crawl up a more realistic gradient of say 30 degrees, lets say 4000lbft, then with a 4ft long wishbone I know that the lifting force would be 1000lb, which may in the antisquat scheme of things on avehicle weighing 4000lbs be equivelant to two tenths of bugger all.
    Yes I'm ovethinking things, and I don't really NEED to. But it's something that has interested me of late, and a little mental excercise might keep this old brain functioning a bit longer.
    Wagoo.

  4. #4
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    I've always used the formula as follows:

    I can't get up = It's too steep or too slippery

    Who in the world would try to work it out using a mathematical formula?
    D4 SDV6, a blank canvas

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    Quote Originally Posted by wardy1 View Post
    I've always used the formula as follows:

    I can't get up = It's too steep or too slippery

    Who in the world would try to work it out using a mathematical formula?
    Good one.
    Filed for future reference.

  6. #6
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    Quote Originally Posted by wagoo View Post
    Yes Ben I know that traction will be the limiting factor, unless overloaded, a very tired engine and/or too large a tyre are part of the equation,and i've run out of power on a few occasions for all the above. but that doesn't really answer my question.There are mathematical formulas on the net for calculating climbing abilty but the way they are laid out makes them difficult to follow for this old codger. I'll give you an idea why I would like to know. Unimogs are criticised for having too much antisquat geometry in their torque tube suspension design. If I want to build a vehicle with Unimog axles and a 4ft long one link wishbone to replace the torque tube, I can calculate how much lifting force is applied via the wishbone pivot to the chassis at mid wheelbase for a given amount of axle torque. if I have a formula for calculation how much axle torque is required to crawl up a more realistic gradient of say 30 degrees, lets say 4000lbft, then with a 4ft long wishbone I know that the lifting force would be 1000lb, which may in the antisquat scheme of things on avehicle weighing 4000lbs be equivelant to two tenths of bugger all.
    Yes I'm ovethinking things, and I don't really NEED to. But it's something that has interested me of late, and a little mental excercise might keep this old brain functioning a bit longer.
    Wagoo.
    OK - so you want to calculate anti-squat - a different question. I am no expert on that, but plenty on ol and pirate are. have a read here:
    Outer Limits 4x4 Board • View topic - Anti Squat, anti Dive suspension geometry.
    (and associated links). Be forewarned - lots of great tech but you need a thick skin on pirate.

    From my limited understanding, A single-link suspension like you describe, terminating at the CofG of the vehicle will give 100% AS.

  7. #7
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    Quote Originally Posted by wardy1 View Post
    I've always used the formula as follows:

    I can't get up = It's too steep or too slippery

    Who in the world would try to work it out using a mathematical formula?
    If you've got nothing useful to contribute then kindly move along. There's nothing of interest here for you.
    Wagoo.

  8. #8
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    Quote Originally Posted by isuzurover View Post
    OK - so you want to calculate anti-squat - a different question. I am no expert on that, but plenty on ol and pirate are. have a read here:
    Outer Limits 4x4 Board • View topic - Anti Squat, anti Dive suspension geometry.
    (and associated links). Be forewarned - lots of great tech but you need a thick skin on pirate.

    From my limited understanding, A single-link suspension like you describe, terminating at the CofG of the vehicle will give 100% AS.
    Thanks for the link Ben.That bloke daddylonglegs seems like he's up himself
    Wagoo.

  9. #9
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    Quote Originally Posted by wagoo View Post
    Thanks for the link Ben.That bloke daddylonglegs seems like he's up himself
    Wagoo.
    Bill/daddylonglegs/Agrover/portalrover knows his stuff and has built some of the most innovative landies around - home made portals, home made underdrives, forced articulation, a 6x6 IIA with great wheel travel, etc etc.

  10. #10
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    Quote Originally Posted by isuzurover View Post
    Bill/daddylonglegs/Agrover/portalrover knows his stuff and has built some of the most innovative landies around - home made portals, home made underdrives, forced articulation, a 6x6 IIA with great wheel travel, etc etc.
    Geez,how many user names does one man need? Sorry Ben I thought the penny might have dropped with the smilie at the end of my comment.
    Seriously though,i'm working on something different, and none of the threads on pirate or outers give me what I'm looking for.
    Bilagoo

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