Calculating camber change with suspension travel
Discussion
I'm trying to work out how to calculate the expected camber change on a double wishbone rear suspension.
All the angles, lengths and coordinates are known for the starting condition.
Let's say the bottom bush of the hub is moved up by a specific distance.
How do I calculate the new position of the top bush?
I've tried researching this on the internet without success. Any gurus out there that can help?
All the angles, lengths and coordinates are known for the starting condition.
Let's say the bottom bush of the hub is moved up by a specific distance.
How do I calculate the new position of the top bush?
I've tried researching this on the internet without success. Any gurus out there that can help?
It's possible to calculate it, and you can get software to do it for you (if you don't mind paying) or do the calcs yourself if you can deal with moderately complex trig. But you can get a rough approximation without the trig, if you have a conventional twin wishbone setup with the inboard pivot axis horizontal and parallel to the centerline, and with the lower wishbone roughly level at normal ride height.
The basic approach is to measure the angle (relative to horizontal) and length (from top ball joint to the pivot axis) for the lower wishbone, from that you can calculate the distance moved horizontally when it moves a small distance vertically (e.g. 10mm).
Now assume that the vertical distance travelled is the same at the top ball joint and do the same calculation of the horizontal distance travelled.
By subtracting the two horizontal deflections and knowing the distance between the top/bottom ball joints you can then work out the angular movement of the hub.
Mathematically speaking it's a horrible approximation and if it matters you should do the trig to get the answer accurately, but for small movements and assuming typical dimensions and angles it will put you in the right ball park.
The basic approach is to measure the angle (relative to horizontal) and length (from top ball joint to the pivot axis) for the lower wishbone, from that you can calculate the distance moved horizontally when it moves a small distance vertically (e.g. 10mm).
Now assume that the vertical distance travelled is the same at the top ball joint and do the same calculation of the horizontal distance travelled.
By subtracting the two horizontal deflections and knowing the distance between the top/bottom ball joints you can then work out the angular movement of the hub.
Mathematically speaking it's a horrible approximation and if it matters you should do the trig to get the answer accurately, but for small movements and assuming typical dimensions and angles it will put you in the right ball park.
Thanks for your reply. I'm off out today so will read it fully later.
What I want to do is write a spreadsheet to calculate the camber change for different suspension positions so that I can understand the reprocussions of possible changes to ride height/wheel/tyre size wishbone length and also moving the inner pickup points.
I can do the basic trig, SOHCAHTOA and all that, which allows me to calculate coordinates and angles from a few measurements but I come unstuck trying to calculate where the top bush moves to when I move the bottom one a known amount.
I've looked up about four bar links but have been unable to find the correct equation/technique to help me out.
Any mathmatical clues gratefully recieved.
What I want to do is write a spreadsheet to calculate the camber change for different suspension positions so that I can understand the reprocussions of possible changes to ride height/wheel/tyre size wishbone length and also moving the inner pickup points.
I can do the basic trig, SOHCAHTOA and all that, which allows me to calculate coordinates and angles from a few measurements but I come unstuck trying to calculate where the top bush moves to when I move the bottom one a known amount.
I've looked up about four bar links but have been unable to find the correct equation/technique to help me out.
Any mathmatical clues gratefully recieved.
As GreenV8S says, you can buy programs to do it, though some of them (including the most highly respected 'amateur' package, the 'Mitchell Program' - at least the last time I looked at it; it may have been fixed by now), are fatally flawed in the way they do some of the calculations.
You can sometimes download free 'trial' versions of the programs (try Beven Young or Mitchell Software as a start). Lotus Cars' software division also does a rather nice suite of software (as you'd expect), but make sure you're sitting down with a strong drink in your hand before ringing them to ask the price of a licence.
Alternatively (and the method I use, since I'm an Architect and use the software on a daily basis) is to draw the geometry in CAD and measure it. You can download hooky copies of AutoCAD (the dominant CAD package) free, if you know where to look. It's a complex program and takes a lot of learning, but of course it's usefulness isn't limited to drawing up suspension geometry. The latest versions of AutoCAD allow you to 'constrain' components so that, for instance, you can force the wishbones to rotate only about its chassis pickups and then force the uprights to follow the wishbones, but even with the older versions of AutoCAD that didn;t have the 'constraints' function, you can make it work it out with a little bit more effort.
There is also the option of making up 'paper dollies' or 'string computers', if you prefer not to use computers. See the books 'Competition Car Suspension' by Allan Staniforth or 'Tune To Win' by Carroll Smith for full details.
I've also got an Excel spreadsheet that graphically simulates suspension movement in a similar way to the software packages listed above. I downloaded it from somewhere and have never even used it, so can offer absolutely no guarantees about its accuracy or function, but if you want a copy, contact me via my profile and I'll send it to you.
One note of caution I'd sound on all these techniques is that computer geek's of 'garbage in = garbage out' applies even more than usual. Straight bump/droop is easy enough to analyse, but when you get to roll, you've got to remember that cars do NOT roll around the 'Roll Axis' that links their front and rear geometric roll centres (and they certainly don't roll around a fixed point at ground level, as the Mitchell software assumes
). Due to different front and rear roll stiffnesses, they assume an attitude of 'skewed roll' (ie. a combination of roll and dive/squat), which can make a big difference to the resultant camber angles. Working out the angles of this 'skewed roll' is a whole kettle of fish on its own. 
You can sometimes download free 'trial' versions of the programs (try Beven Young or Mitchell Software as a start). Lotus Cars' software division also does a rather nice suite of software (as you'd expect), but make sure you're sitting down with a strong drink in your hand before ringing them to ask the price of a licence.
Alternatively (and the method I use, since I'm an Architect and use the software on a daily basis) is to draw the geometry in CAD and measure it. You can download hooky copies of AutoCAD (the dominant CAD package) free, if you know where to look. It's a complex program and takes a lot of learning, but of course it's usefulness isn't limited to drawing up suspension geometry. The latest versions of AutoCAD allow you to 'constrain' components so that, for instance, you can force the wishbones to rotate only about its chassis pickups and then force the uprights to follow the wishbones, but even with the older versions of AutoCAD that didn;t have the 'constraints' function, you can make it work it out with a little bit more effort.
There is also the option of making up 'paper dollies' or 'string computers', if you prefer not to use computers. See the books 'Competition Car Suspension' by Allan Staniforth or 'Tune To Win' by Carroll Smith for full details.
I've also got an Excel spreadsheet that graphically simulates suspension movement in a similar way to the software packages listed above. I downloaded it from somewhere and have never even used it, so can offer absolutely no guarantees about its accuracy or function, but if you want a copy, contact me via my profile and I'll send it to you.
One note of caution I'd sound on all these techniques is that computer geek's of 'garbage in = garbage out' applies even more than usual. Straight bump/droop is easy enough to analyse, but when you get to roll, you've got to remember that cars do NOT roll around the 'Roll Axis' that links their front and rear geometric roll centres (and they certainly don't roll around a fixed point at ground level, as the Mitchell software assumes
). Due to different front and rear roll stiffnesses, they assume an attitude of 'skewed roll' (ie. a combination of roll and dive/squat), which can make a big difference to the resultant camber angles. Working out the angles of this 'skewed roll' is a whole kettle of fish on its own. Edited by Sam_68 on Monday 31st August 09:40
Thanks Sam
I know exactly what you mean with 'garbage in = garbage out' which is why I want to calculate it for myself as opposed to using someone else's program or massively complex spreadsheet. At least it's my own garbage then! I can live with that.
I've got the Staniforth and Smith books plus the extortionately expensive Milliken tome but none of them really explain the maths behind the geometry which I think is a bit of a cop out.
String computers obviously work well enough but it doesn't de-mystify what is going on like a mathematical equation. I'm in the pursuit of understanding rather than "just" solving the problem.
I purchased a cheap but legal copy of turbo cad but frankly found it so un-intuitive to learn that I gave up after about five hours. Plus the "'constrain' components" feature you mention is restricted to the more expensive pro variant which I can't justify.
I find it frustrating that I can write a spreadsheet which can calculate all the information from a few measured positions but when I move one point there are too many unknowns for basic trig and my simple brain to work out where the other point is.
BTW my first application of the new spreadsheet is for a Wedge which does not have its "inboard pivot axis horizontal and parallel to the centerline" and I don't think the "lower wishbone is roughly level at normal ride height"
I know exactly what you mean with 'garbage in = garbage out' which is why I want to calculate it for myself as opposed to using someone else's program or massively complex spreadsheet. At least it's my own garbage then! I can live with that.
I've got the Staniforth and Smith books plus the extortionately expensive Milliken tome but none of them really explain the maths behind the geometry which I think is a bit of a cop out.
String computers obviously work well enough but it doesn't de-mystify what is going on like a mathematical equation. I'm in the pursuit of understanding rather than "just" solving the problem.
I purchased a cheap but legal copy of turbo cad but frankly found it so un-intuitive to learn that I gave up after about five hours. Plus the "'constrain' components" feature you mention is restricted to the more expensive pro variant which I can't justify.
I find it frustrating that I can write a spreadsheet which can calculate all the information from a few measured positions but when I move one point there are too many unknowns for basic trig and my simple brain to work out where the other point is.
BTW my first application of the new spreadsheet is for a Wedge which does not have its "inboard pivot axis horizontal and parallel to the centerline" and I don't think the "lower wishbone is roughly level at normal ride height"
leorest said:
...none of them really explain the maths behind the geometry which I think is a bit of a cop out... I'm in the pursuit of understanding rather than "just" solving the problem.
If you really want to wade through the maths, I'm pretty sure I've got a copy of RaceTech magazine somewhere that goes through it in detail. I must admit, I've always been happy to merely have the tools with which to calculate a solution and have never felt the need to actually understand the mathematical nuts and bolts of those tools, but if you give me couple of days I'm sure I could dig it out of my archive, scan it and mail it to you. Again, contact me via my profile if you're interested.leorest said:
...I purchased a cheap but legal copy of turbo cad but frankly found it so un-intuitive to learn that I gave up after about five hours.
Don't confuse TurboCad with AutoCAD... the former is a cheap toy, even compared to AutoCAD LT (LighT). I'm fortunate enough to have the latest copy of AutoCAD provided to me with each update by my employer, but I'm aware that it's easy enough to get hold of 'cracked' copies on the internet. I wouldn't call AutoCAD counter-intuitive, but it is massively powerful and complex, so does take a lot of learning before you are truly proficient; I've been using it regularly for about 12 years, and I'm still learning new wrinkles.Sam_68 said:
leorest said:
...none of them really explain the maths behind the geometry which I think is a bit of a cop out... I'm in the pursuit of understanding rather than "just" solving the problem.
If you really want to wade through the maths, I'm pretty sure I've got a copy of RaceTech magazine somewhere that goes through it in detail. I must admit, I've always been happy to merely have the tools with which to calculate a solution and have never felt the need to actually understand the mathematical nuts and bolts of those tools, but if you give me couple of days I'm sure I could dig it out of my archive, scan it and mail it to you. Again, contact me via my profile if you're interested.leorest said:
...I purchased a cheap but legal copy of turbo cad but frankly found it so un-intuitive to learn that I gave up after about five hours.
Don't confuse TurboCad with AutoCAD... the former is a cheap toy, even compared to AutoCAD LT (LighT). I'm fortunate enough to have the latest copy of AutoCAD provided to me with each update by my employer, but I'm aware that it's easy enough to get hold of 'cracked' copies on the internet. I wouldn't call AutoCAD counter-intuitive, but it is massively powerful and complex, so does take a lot of learning before you are truly proficient; I've been using it regularly for about 12 years, and I'm still learning new wrinkles.Thanks for offering to take the time to dig out the information. I'll drop you an email later when I get home. I'm sure I just need a nudge in the right direction.
Try:
http://www.racingaspirations.com/?p=286
I was going to make my own animation a while ago, but that site serves most purposes I think.
http://www.racingaspirations.com/?p=286
I was going to make my own animation a while ago, but that site serves most purposes I think.
spend said:
Try:
http://www.racingaspirations.com/?p=286
I was going to make my own animation a while ago, but that site serves most purposes I think.
That is interesting. It's a shame it doesn't allow values to be typed in...http://www.racingaspirations.com/?p=286
I was going to make my own animation a while ago, but that site serves most purposes I think.
I'm still holding out for some mathematical inspiration.
Just pinged an email to Sam
Its not hard, there should be online theorums to calc intersection of the 2 prescribed circles. IIRC:
you know r0 r1, calc the length of d (a + b), h is the same & then
a = ( r0^2 - r1^2 + d^2 )/2d
I have a perl script somewhere that I was playing with to do the animation as in illustration, but lost interest explaining simple geometric effects to brain dead keyboard warriors
Explaining how to install perl + tk was too much of a PITA to winbods as well 
you know r0 r1, calc the length of d (a + b), h is the same & then
a = ( r0^2 - r1^2 + d^2 )/2d
I have a perl script somewhere that I was playing with to do the animation as in illustration, but lost interest explaining simple geometric effects to brain dead keyboard warriors
Explaining how to install perl + tk was too much of a PITA to winbods as well leorest said:
I'm still holding out for some mathematical inspiration.
Just pinged an email to Sam
Received.Just pinged an email to Sam
I've dug out the relevant magazine article (Racetech #18, June/July '98) and I'll try to find time to scan it to .pdf for you at work tomorrow.
The 'vector tetrahedron problem' is what you're trying to solve, apparently, and it can be dealt with by means of standard quadratic equations.
Sounds like hours of fun... I think I'll stick to AutoCAD!
Edited by Sam_68 on Tuesday 1st September 21:30
spend said:
Its not hard, there should be online theorums to calc intersection of the 2 prescribed circles.
Surely that only does for 2-dimensions? Fine if you've got no anti-dive/anti squat, and the pick-ups are parallel to the chassis centreline...Must admit, I'm happy with my computerised paper dollies, though - end results is all I'm interested in - I'll leave the hard stuff to you chaps!
spend said:
Its not hard, there should be online theorums to calc intersection of the 2 prescribed circles. IIRC:
you know r0 r1, calc the length of d (a + b), h is the same & then
a = ( r0^2 - r1^2 + d^2 )/2d
I have a perl script somewhere that I was playing with to do the animation as in illustration, but lost interest explaining simple geometric effects to brain dead keyboard warriors Explaining how to install perl + tk was too much of a PITA to winbods as well
Nothing's hard when you know how...you know r0 r1, calc the length of d (a + b), h is the same & then
a = ( r0^2 - r1^2 + d^2 )/2d
I have a perl script somewhere that I was playing with to do the animation as in illustration, but lost interest explaining simple geometric effects to brain dead keyboard warriors
Explaining how to install perl + tk was too much of a PITA to winbods as well Thanks I'm off Googling "calculating intersection of the 2 prescribed circles"
leorest : do i assume correctly that you have a car and you're trying to work out the geo changes ..? if you have the car why not just measure it? I regularly measure cars up by taking the springs off and putting a trolley jack under each corner, you can pitch and roll your car to your heart's content in real-time so to speak (ok so you can't introduce simulated bush deflection and tyre distortions under significant load, but if it's the geo you're interested in it'll save you tapping keys: introduce a roll angle and measure the camber changes actually on the car, introduce a squat element and measure the camber change again etc etc. Once youve done (Quite a few) measurements within the limits of your damper travel you'll have a pretty good idea what's going on . admittedly it does involve you actually doing some dirtier work than tapping keys!)
spitfire4v8 said:
...admittedly it does involve you actually doing some dirtier work than tapping keys!
It also involves having a car to measure!Not much use if you're trying to design something from scratch, or if you're trying to work out the effect that you'd get from modifications to an existing geometry. It also doesn't tell you anything about roll centre location, which is arguably more important than camber.
Edited by Sam_68 on Tuesday 1st September 22:02
Yes, fair enough - as you say, if all you want to know is the camber change on an existing set-up, then simply measuring it is the easiest way.
By the sound of it, he's after a more complete theoretical understanding than even I'd be interested in pursuing, though. Could be useful if you could use it to 'reverse engineer' the geometry from a specified camber curve and roll centre location, but there'll be some pretty tough maths to confront to achieve that!
By the sound of it, he's after a more complete theoretical understanding than even I'd be interested in pursuing, though. Could be useful if you could use it to 'reverse engineer' the geometry from a specified camber curve and roll centre location, but there'll be some pretty tough maths to confront to achieve that!
Yes I can and will measure it but it helps to make some predictions first to check that the measurements are sensible. It's also useful to be able to do some "what if" scenarios for changes in ride height or moving the top hard point which is easy to do on my vehicle. If any of that is sensible to do is yet to be seen;)
I'm not looking to fundamentally change the setup more to understand it and be able to make informed adjustments without introducing unexpected nasties. I'm not convinced the correct shims are fitted to the driveshaft(top link) so I know I will be looking into resetting camber at the very least.
The formula for calculating the intersection of two circles looks like how to solve the problem.
Thanks again
I'm not looking to fundamentally change the setup more to understand it and be able to make informed adjustments without introducing unexpected nasties. I'm not convinced the correct shims are fitted to the driveshaft(top link) so I know I will be looking into resetting camber at the very least.
The formula for calculating the intersection of two circles looks like how to solve the problem.
Thanks again
Noting the change in camber per mm of deflection I found quite interesting BTW. You can also play with wishbone lengths if you are considering making some of your own / alternate uprights. Its also interesting plotting the damper deflection against wheel deflection whilst you are at it IMHO.
Since it probably bores most folks feel free to give me a shout, but if you have understood that you fix the pivot from lower wishbone and use the the theorem I hinted at you should be able to solve just about everything IIRC.
Since it probably bores most folks feel free to give me a shout, but if you have understood that you fix the pivot from lower wishbone and use the the theorem I hinted at you should be able to solve just about everything IIRC.
Sam_68 said:
Received.
I've dug out the relevant magazine article (Racetech #18, June/July '98) and I'll try to find time to scan it to .pdf for you at work tomorrow.
The 'vector tetrahedron problem' is what you're trying to solve, apparently, and it can be dealt with by means of standard quadratic equations.
Sounds like hours of fun... I think I'll stick to AutoCAD!
I don't want to take up too much of your time but that sounds interesting and I look forward to seeing it.I've dug out the relevant magazine article (Racetech #18, June/July '98) and I'll try to find time to scan it to .pdf for you at work tomorrow.
The 'vector tetrahedron problem' is what you're trying to solve, apparently, and it can be dealt with by means of standard quadratic equations.
Sounds like hours of fun... I think I'll stick to AutoCAD!
Edited by Sam_68 on Tuesday 1st September 21:30
As for doing it in AutoCAD well that would be luxury but that's not available to me I'm stuck with a rule and some maths.
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