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CG/Rollover calculator

WaterH

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I've been thinking about something for awhile now. (Dangerous I know) I would like to know the angle that my project truck could take on a side hill without tipping over. I'd like to make an inclination meter for the dash. I think I could devise a test to determine the angle, but it would be kind of a PITA to do. Then I got wondering if you couldn't figure it out with some scales. Let me explain.

Lets say we have a hypothetical vehical. For this discussion, we'll say the tires are "rock hard" and the axles are bolted to the frame. (No suspension) It is 6' wide from the outside of the tire treads. It weighs 4000 lbs. it has perfect weight distribution and the CG is 3' off the ground. If we tip one side up 45 degrees, there will be 4000 lbs. on the two downside tires and no weight on the upside tires. If we were to tip it 46 degrees, it would rollover. First, does everybody agree this would be true? If not, explain.

Assuming this is correct, I'm thinking that we could work backwards by weighing the machine flat on the ground and then again with one side tipped up a fixed amount. Let's say 15 degrees. A certain amount of weight would transfer to the low side tires. I'm thinking that we could make a calculator that we could feed in the total weight and the weight transfer and it could tell us how high the CG is and the ultimate "tipover" angle.

I realize that angle would be less because the "real world" tires at low psi and soft suspension would increase the weight transfer, but it should be close.

Now, I think I could come up with an equation to accomplish this, but it would be nice if one of you "computer wiz" guys could make a calculator that we just feed the data in like a link calculator or the ratio calculator.

PS, I think the mods here should put sticky for the link calculator and the "Grim Jeeper" ratio calculator. If this works out, it also could be put in a sticky.


Comments and flames welcome.
 

Byro

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Seems like a mathematical nightmare. Bust out the forklift and a magnetic angle finder on the dash and find out exactly.
 

gt1guy

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The proper way to determine your CG accurately will have your vehicle a foot or two from finding the rollover angle. Pretty easy at that point to find the tipping point.

Getting the correct CG is the hard part in what your asking. Bad numbers put in a calculator = bad results
 

ExWrench

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Seems like a mathematical nightmare. Bust out the forklift and a magnetic angle finder on the dash and find out exactly.

If you do this^ - run a safety strap or chain from near-side frame rail to forklift's load backrest in case you pass the tipping point. Unless you go apeshit overboard, the strap or chain will only see ~100# of tension when just over-center.
 

WaterH

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Seems like a mathematical nightmare. Bust out the forklift and a magnetic angle finder on the dash and find out exactly.

Doesn't seem that hard to me. I did forget something. You would need to account for the width of the vehical. So I'm thinking you need three things.

Width from outside tire tread edge to outside tire tread edge.

Total Weight when flat on ground.

Weight transfer to low side tires. (At some specific angle)


There would be some error due to one side being heavier than the other. (Drivers or pax side diff) But I wouldn't think that would be dramatic.
 

vetteboy79

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In NJ we have 'modified height vehicle' inspections...part of it was weighing the vehicle on flat ground, then you drove one side up onto a concrete berm, and they measured the amount of weight transfer to the downhill tires. If it exceeded a certain amount you'd fail inspection, this was known as the 'tilt test' or stability test.

I forget what the threshold was or how it was calculated, but yes what you're asking for can be done in theory.
 

Ghetto Fab.

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I had friends that did something similar in their senior project in college. They used scales to determine fore and aft, as well as side to side weight balance, but they also needed the height. The solution was to use scales on the rear tires and a forklift to lift the front up. With the front tires a known height off the ground and a now known weight transfer to the back tires, the CG height could be calculated. As I recall they had to get the front 4-5ft off the ground. I don't see why that wouldn't work side to side also. Also, if you know the cg height you can figure out the tipping angle and vice versa. I could probably dig up the math on the above project if needed.

Kevin
 

WaterH

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I had friends that did something similar in their senior project in college. They used scales to determine fore and aft, as well as side to side weight balance, but they also needed the height. The solution was to use scales on the rear tires and a forklift to lift the front up. With the front tires a known height off the ground and a now known weight transfer to the back tires, the CG height could be calculated. As I recall they had to get the front 4-5ft off the ground. I don't see why that wouldn't work side to side also. Also, if you know the cg height you can figure out the tipping angle and vice versa. I could probably dig up the math on the above project if needed.

Kevin

I might be thinking wrong, but it would seem like it wouldn't work fore and aft because of overhang front and back. There really isn't any over hang side to side. The reason it wouldn't seem to work with overhang is because that weight would never shift to the low side tires until you were near vertical. Again, Maybe I'm thinking wrong here.

in any case, my friend just got some racing car scales in an estate sale. I maybe borrowing them if they work.
 

CDA 455 II

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:laughing::flipoff2:

fetch?id=6415&d=1590124130.gif
 

Crimsen

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How do you think that these people are going to obtain the wight on each tire to start plugging those numbers into a calculator?
 

WaterH

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How do you think that these people are going to obtain the wight on each tire to start plugging those numbers into a calculator?

I hate to be sarcastic, but maybe they would use some kind of scale.


So, my first thought is take the transferred weight and make it a percentage of the total. In the case of my hypothetical truck from the first post, the weight transfered was 50 percent of the total. (At 45 degrees) If I take 50 percent of the width (72"), I come up with 36" for a height to the CG. Could it be that simple?

Of course that only works at 45 degrees, but I think I could make an equation account for a lesser angle. Let me ask a question. If 2000 lbs. transfers to the lower tires at 45 degrees, would I assume 1000 lbs. to transfer at 22.5 degrees? Or do you think the weight transfer would not be linear?
 

gt1guy

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This might help. It can be done side to side also.

This comes from
www.longacreracing.com





CENTER OF GRAVITY HEIGHT



Finding the center of gravity height can be done in several ways, none of which are accomplished very easily and without some work. Presented here is the easiest method. The center of gravity height is calculated by weighing the car when level and then raising the car at least 10 inches at the rear and weighing the front again. Enter the data into the program below to calculate your center of gravity height.

Before you begin:
  • Be sure that all fluids are full
  • Replace each shock absorber with a solid link to eliminate suspension travel
  • Make sure the tires are inflated to the maximum pressure as specified by the manufacturer to eliminate any sidewall flex
Note: If these steps are not taken, the calculations will be inaccurate
Center of Gravity Height Formula Definition of Variables

  • CGH - Center of Gravity Height
  • WB - Wheelbase (inches)
  • TW - Total weight
  • FW1 - Front weight LEVEL
  • FW2 - Front weight RAISED
  • FWc - FW2 - FW1 (change in weights)
  • HT - Height raised (inches)
  • Adj - Adjacent side (see below)
  • Tan q - Tangent of angle (see below)
  • CLF - Left Front tire circumference
  • CRF - Right Front tire circumference
  • C - (CLF + CRF) / 2 (average circumference)
  • r - Axle Height
Related Formulas

 

WaterH

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Interesting. I notice they don't account for overhang, so I guess it doesn't matter. I don't follow the theory behind the circumference of tires. I realize a racing car could have differnt height tires. Maybe they do that if your WB is measured at the axle center. Then the staggered heights might make a slight differnce in the true WB. Wouldn't really matter side to side.

The idea of locking the shocks is interesting. They say at least 10". I'm not sure if you need more or less for a side to side measurement. (Because of the shorter width vs WB)
 

'84 Bronco II

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This might help. It can be done side to side also.

This comes from
www.longacreracing.com





CENTER OF GRAVITY HEIGHT



Finding the center of gravity height can be done in several ways, none of which are accomplished very easily and without some work. Presented here is the easiest method. The center of gravity height is calculated by weighing the car when level and then raising the car at least 10 inches at the rear and weighing the front again. Enter the data into the program below to calculate your center of gravity height.

Before you begin:
  • Be sure that all fluids are full
  • Replace each shock absorber with a solid link to eliminate suspension travel
  • Make sure the tires are inflated to the maximum pressure as specified by the manufacturer to eliminate any sidewall flex
Note: If these steps are not taken, the calculations will be inaccurate
Center of Gravity Height Formula Definition of Variables

  • CGH - Center of Gravity Height
  • WB - Wheelbase (inches)
  • TW - Total weight
  • FW1 - Front weight LEVEL
  • FW2 - Front weight RAISED
  • FWc - FW2 - FW1 (change in weights)
  • HT - Height raised (inches)
  • Adj - Adjacent side (see below)
  • Tan q - Tangent of angle (see below)
  • CLF - Left Front tire circumference
  • CRF - Right Front tire circumference
  • C - (CLF + CRF) / 2 (average circumference)
  • r - Axle Height
Related Formulas


This is correct.

Here it is derived:

Step 1
2020-05-24 11-58.jpeg



Step 2
2020-05-24 12-13.jpeg
 

vetteboy79

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The idea of locking the shocks is interesting. They say at least 10". I'm not sure if you need more or less for a side to side measurement. (Because of the shorter width vs WB)

For what it's worth - in the stability test thing I mentioned here in NJ, (and for the purposes of what you're trying to do), you don't want the shocks locked out. The whole point is that the CG shifts because we have these long-travel, floppy suspensions. Knowing the static location of the CG on level ground isn't all that helpful for knowing your tipover angle as it'll shift as the body moves around the suspension.

Overall height is not really an issue in NJ as there are already other limitations for that; the point of the stability test is to see if your suspension is extra-floppy to the point that too much weight % gets transferred for a given incline.
 

Beat95yj

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Interesting. I notice they don't account for overhang, so I guess it doesn't matter. I don't follow the theory behind the circumference of tires. I realize a racing car could have differnt height tires. Maybe they do that if your WB is measured at the axle center. Then the staggered heights might make a slight differnce in the true WB. Wouldn't really matter side to side.

The idea of locking the shocks is interesting. They say at least 10". I'm not sure if you need more or less for a side to side measurement. (Because of the shorter width vs WB)

Overhang is a relevant the center of gravity does not change whether there’s overhang or not if it’s evenly distributed.
 

ExWrench

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. . . in the stability test . . . you don't want the shocks locked out.
The . . . CG shifts because . . . long-travel, floppy suspensions.
. . . CG on level . . . isn't all that helpful for knowing your tipover angle . . .

Important point there^.
CG is handy information / cool to know, but don't use it for theoretical stability calculations.
Once the suspension sacks over & tire sidewalls wallow, tipping points won't be near theoretical.

If you want absolute certainty, pick up 1 side at a time to find the tipping points in each direction.
Actual tire pressure (maybe do tests aired up & aired down), loaded rig, driver / pax weight, etc.
Run safety strap / rope / chain on side being elevated to prevent tipover. Or film it & post here:laughing:
 

Austin

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That angle would be nice to know .. and great if it's RC ... just don't ever get in or put gear in it....
 

WaterH

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For what it's worth - in the stability test thing I mentioned here in NJ, (and for the purposes of what you're trying to do), you don't want the shocks locked out. The whole point is that the CG shifts because we have these long-travel, floppy suspensions. Knowing the static location of the CG on level ground isn't all that helpful for knowing your tipover angle as it'll shift as the body moves around the suspension.

Overall height is not really an issue in NJ as there are already other limitations for that; the point of the stability test is to see if your suspension is extra-floppy to the point that too much weight % gets transferred for a given incline.


I suppose you could do the CG calculation with the shocks locked and unlocked. The first would tell you the actual CG and the second would be more useful for the tipover info. In my first post I said I would subtract a few degrees to account for suspension and single digit tire pressure. But it would be nice to know how many degrees is appropriate.

In my case, I could do the calculation with my airbags jacked up on the side that I jack the tires up and do another calculation.

I just thought of something. If the purpose of this exercise is to mount a inclometer on the dash, the suspension doesn't really matter. Assuming you have a "red zone", the suspension will just get you there quicker. For example, if the calculation says tipover at 45 degrees and you drive on a 38 degree side hill. The suspension flops another six degrees, your inclometer will read 44 degrees and you better be careful. The fact that the tires are not actually at 44 degrees will give you some extra wiggle room.
 

WaterH

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That angle would be nice to know .. and great if it's RC ... just don't ever get in or put gear in it....

That is another sobering thought. Lol. I guess it wouldn't hurt to do one more calculation with the expected camping weight. (In the correct location)
 

Crimsen

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I hate to be sarcastic, but maybe they would use some kind of scale.


So, my first thought is take the transferred weight and make it a percentage of the total. In the case of my hypothetical truck from the first post, the weight transfered was 50 percent of the total. (At 45 degrees) If I take 50 percent of the width (72"), I come up with 36" for a height to the CG. Could it be that simple?

Of course that only works at 45 degrees, but I think I could make an equation account for a lesser angle. Let me ask a question. If 2000 lbs. transfers to the lower tires at 45 degrees, would I assume 1000 lbs. to transfer at 22.5 degrees? Or do you think the weight transfer would not be linear?


your right, a scale will measure the weight. But where do you get a scale that measures 1500-2000 lbs with any real accuracy that will be widely available to the people who are going to use this calculator? Not sure what kind of bathroom scale your wife/girlfriend/SO uses but that is probably out of the question. :flipoff2:Not sure how kindly the local weigh scales will take to you jacking up a vehicle partially on their scale to get the measurements.
 

WaterH

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your right, a scale will measure the weight. But where do you get a scale that measures 1500-2000 lbs with any real accuracy that will be widely available to the people who are going to use this calculator? Not sure what kind of bathroom scale your wife/girlfriend/SO uses but that is probably out of the question. :flipoff2:Not sure how kindly the local weigh scales will take to you jacking up a vehicle partially on their scale to get the measurements.

Jegs has them for $200

I happen to have a scale on my gantry Crane that weighs up to 2500 lbs. with good accuracy. Might take some fancy rigging to use it. But I already mentioned my friend just got a set of racing car scales. Are racing car scales that rare in your parts? In any case, is it more likely that somebody is going to have a forklift capable of proforming a tipover test? While I think you could do a test like that safely, it would be lots easier to do the scales safely.
 

Crimsen

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Jegs has them for $200

I happen to have a scale on my gantry Crane that weighs up to 2500 lbs. with good accuracy. Might take some fancy rigging to use it. But I already mentioned my friend just got a set of racing car scales. Are racing car scales that rare in your parts? In any case, is it more likely that somebody is going to have a forklift capable of proforming a tipover test? While I think you could do a test like that safely, it would be lots easier to do the scales safely.



up here in the great white north, yea, not a whole lot of options that i have seen. Have not really put a ton of effort in to finding one since i have had nonuse yet, but never seen anything in flyers or websites. May have to take a look at jegs and see what they got. I imagine crane places up here carry things like that but i would also expect since its a lifting device, you have the specialty market “tax” and life safety “tax” that makes it something more for a business than for a hobbiest.
 

tracyb

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up here in the great white north, yea, not a whole lot of options that i have seen. Have not really put a ton of effort in to finding one since i have had nonuse yet, but never seen anything in flyers or websites. May have to take a look at jegs and see what they got. I imagine crane places up here carry things like that but i would also expect since its a lifting device, you have the specialty market “tax” and life safety “tax” that makes it something more for a business than for a hobbiest.

a scale really shouldn't be too hard for most people to find. heres a hanging scale i use in the shop all the time and it is very accurate. i use it for everything from weighing Co2 tanks while filling to weighing cars.

$100 good to 2k lbs
https://www.amazon.com/dp/B077Q7HVZ7...xpY2s9dHJ1ZQ==
 

arse_sidewards

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your right, a scale will measure the weight. But where do you get a scale that measures 1500-2000 lbs with any real accuracy that will be widely available to the people who are going to use this calculator? Not sure what kind of bathroom scale your wife/girlfriend/SO uses but that is probably out of the question. :flipoff2:Not sure how kindly the local weigh scales will take to you jacking up a vehicle partially on their scale to get the measurements.

You don't.

You lift up one side with your scale. When your scale reads 0 then it's balancing on the two wheels that are on the ground and that's your angle.

If you want a margin of safety then scale the vehicle at the truck stop and record the angle when there's X% of that left on the scale you're lifting with.
 

Harry Johnson

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I hope all you math geniuses also took a course in hydrodynamics to account for when your shitty cooler full of melted ice and lukewarm silver bullets sloshes all the way up the cooler wall while you're in party mode up backdoor... otherwise what are we even doing here?:flipoff2:
 

gt1guy

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I suppose you could do the CG calculation with the shocks locked and unlocked. The first would tell you the actual CG and the second would be more useful for the tipover info. In my first post I said I would subtract a few degrees to account for suspension and single digit tire pressure. But it would be nice to know how many degrees is appropriate.

In my case, I could do the calculation with my airbags jacked up on the side that I jack the tires up and do another calculation.

I just thought of something. If the purpose of this exercise is to mount a inclometer on the dash, the suspension doesn't really matter. Assuming you have a "red zone", the suspension will just get you there quicker. For example, if the calculation says tipover at 45 degrees and you drive on a 38 degree side hill. The suspension flops another six degrees, your inclometer will read 44 degrees and you better be careful. The fact that the tires are not actually at 44 degrees will give you some extra wiggle room.


You really do need to separate the CG and tippy testing into two different items. They're two completely different things.

If all you want to do is make a no-go mark on a incline-o-meter, all you need to do is raise one side till it wants to tip.....................then make your mark. The more accurately you have the rig loaded out, the more accurate your mark will be. You don't need to know where your CG is, because it is where it is, you just want to see the results of where it is.

I must have misread your OP. I was thinking you wanted to make a calculator that would tell you the tipping point. Input info= tells you tipping point.
 

WaterH

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You really do need to separate the CG and tippy testing into two different items. They're two completely different things.

If all you want to do is make a no-go mark on a incline-o-meter, all you need to do is raise one side till it wants to tip.....................then make your mark. The more accurately you have the rig loaded out, the more accurate your mark will be. You don't need to know where your CG is, because it is where it is, you just want to see the results of where it is.

I must have misread your OP. I was thinking you wanted to make a calculator that would tell you the tipping point. Input info= tells you tipping point.

Some people may want their exact CG for bragging rights or future modifications. I really don't care about that. My concern is the tipover. When I say that, it doesn't mean I plan to take it to the exact point on the trail. If you look at my first post, I say I plan to subtract a few degrees for suspension and tire pressure. After this discussion, I might be inclined to subtract some for load too. I think everyone should figure as best they can, and then build in a safety margin they are happy with.

At at this point, I could see doing the calculation empty and again with the highest expected load. (In the correct location.) I'm very courious how much, say, 400 lbs. of gear in the bed would make. It might be no big deal. Once somebody does this, they can report back how important it is. I have done CG calculations many times on aircraft. 10 percent is not a big deal. But of course we're talking two differnt things.

In any case, I still think a calculator like this is way simpler/safer than a tip test. The statement "all you need to do is raise one side till it wants to tip" is a hell of a lot harder to set up than weighing the truck a couple times.
 
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