# How can I model the response of a car to a sharp steering input?

April 27, 2016 7:04 PM Subscribe

I'm doing some work for an engineering company that certifies modifications to cars.
One of the tests that they perform is a lane change manoeuvre test. This test simulates an emergency lane change and back to the original lane to prove the stability of the vehicle.
Given testing is relatively expensive (as it involves hiring a suitable facility), and involves some risk to the test driver, they have asked me to come up with a spreadsheet or similar that they can use to have a high level of confidence that the test will be safe before they leave the workshop. i don't know how to do that.

The test is required in NSW for cars that have had a significant change of rated gross mass or centre of gravity location.

The exact test details are here (test code LT2) if you are really interested.

Besides being beyond my capabilities, one of the more powerful computational modelling packages wouldn’t be useful for them in the future, so I'm hoping to do this in Excel.

I have:

Vehicle weight

Vehicle wheel track

Vehicle wheel base

Test speed

Assumed test sideways acceleration (0.6g-0.8g)

I can use a set of scales to determine CG position longitudinally and laterally, and can calculate CG height by re-weighing with front wheels raised.

For initial use I was thinking that an assumed spring rate would be OK.

I can calculate smallest radius turn that the vehicle can make at a particular speed without tipping, but that is different to a quick steering input.

It’s been too long since university days, and I can’t say I really grokked dynamics anyways. Is there a way I can easily model the car and test to determine the approximate response to the steering input?

Thanks heaps

The test is required in NSW for cars that have had a significant change of rated gross mass or centre of gravity location.

The exact test details are here (test code LT2) if you are really interested.

Besides being beyond my capabilities, one of the more powerful computational modelling packages wouldn’t be useful for them in the future, so I'm hoping to do this in Excel.

I have:

Vehicle weight

Vehicle wheel track

Vehicle wheel base

Test speed

Assumed test sideways acceleration (0.6g-0.8g)

I can use a set of scales to determine CG position longitudinally and laterally, and can calculate CG height by re-weighing with front wheels raised.

For initial use I was thinking that an assumed spring rate would be OK.

I can calculate smallest radius turn that the vehicle can make at a particular speed without tipping, but that is different to a quick steering input.

It’s been too long since university days, and I can’t say I really grokked dynamics anyways. Is there a way I can easily model the car and test to determine the approximate response to the steering input?

Thanks heaps

*I can calculate smallest radius turn that the vehicle can make at a particular speed without tipping*

I know this is not quite right but if you assume an instantaneous change in the steering doesn't this define two circles, one with an center to the left and slightly back and straightening out to the new lane a circle with the center to the right and a bit forward. If that's larger than the tipping radius it's safe.

posted by sammyo at 7:37 PM on April 27, 2016 [1 favorite]

(off my phone now)

IANYVehicleDynamicsE, but for a first order "is it worth even going out to the track" approximation, here's how I'd do it:

assuming that the primary criteria is the vehicle not skid, you need to find the smallest turning circle at a particular speed where the side forces on each tyre don't exceed the opposing friction. you then model the lane change as 2 turns, one to leave the current lane and one to straighten out in the new lane.

ground contact area for each tyre will be some function of inflation pressure and wheel load - I have no idea where you get that (the tyre manufacturer?). friction coefficient depends on the tyre, the road surface, and the conditions (is it wet?) - I don't know where you get that either.

then, given the vehicle speed and CG location, you can determine the load on each tyre for a particular turning radius (outer tyres will be more heavily loaded). from this you get the contact areas, from that you get the per-tyre static friction. sum the maximum side force from each tyre, and if that's greater than the force required to turn the vehicle at the radius you're interested in, then no skid.

posted by russm at 7:54 PM on April 27, 2016 [1 favorite]

IANYVehicleDynamicsE, but for a first order "is it worth even going out to the track" approximation, here's how I'd do it:

assuming that the primary criteria is the vehicle not skid, you need to find the smallest turning circle at a particular speed where the side forces on each tyre don't exceed the opposing friction. you then model the lane change as 2 turns, one to leave the current lane and one to straighten out in the new lane.

ground contact area for each tyre will be some function of inflation pressure and wheel load - I have no idea where you get that (the tyre manufacturer?). friction coefficient depends on the tyre, the road surface, and the conditions (is it wet?) - I don't know where you get that either.

then, given the vehicle speed and CG location, you can determine the load on each tyre for a particular turning radius (outer tyres will be more heavily loaded). from this you get the contact areas, from that you get the per-tyre static friction. sum the maximum side force from each tyre, and if that's greater than the force required to turn the vehicle at the radius you're interested in, then no skid.

posted by russm at 7:54 PM on April 27, 2016 [1 favorite]

i think this is going to be hard, in that you're going to need to model everything as coupled, damped oscillators (whose parameters depend on the not just the weight distribution, but the detailed dynamics of the suspension) and even then it's not clear exactly what the conditions are for failure.

the test is looking at the response (described very subjectively in terms of "handling" - not necessarily skidding, or tipping over, but "drivability" according to a test driver) of the car to four turns, with different spacing between them. you think of the car as a plate of jelly, and the turns as impulses, with the test looking at the cumulative effect of the impulses on how the jelly wobbles. but the jelly in this case is not homogeneous - the spring constants and damping are going to vary with direction (more compliance vertically, for example).

presumably in the worst case the impulses will constructively interfere at resonant frequencies (short, violent turns are going to contain a broad spectrum of frequencies) to give the largest response. so

it's such a complex problem i don't see a simple approximation. but maybe something simple and obvious will come out once you start pulling it apart.

tbh i find the whole approach odd. who quoted for this? maybe they had an idea of what to do?

it might be better - if you have the data - to just fit some kind of model to existing data, without trying to understand the physics in any detail (think neural nets). but that is likely ging to need more data than you have. perhaps there is some half-way point where you do a crude analysis of the physics to give a model that is then fitted to existing data...

or ask some smart physics students. smarter then me at any rate.

posted by andrewcooke at 5:19 AM on April 28, 2016

the test is looking at the response (described very subjectively in terms of "handling" - not necessarily skidding, or tipping over, but "drivability" according to a test driver) of the car to four turns, with different spacing between them. you think of the car as a plate of jelly, and the turns as impulses, with the test looking at the cumulative effect of the impulses on how the jelly wobbles. but the jelly in this case is not homogeneous - the spring constants and damping are going to vary with direction (more compliance vertically, for example).

presumably in the worst case the impulses will constructively interfere at resonant frequencies (short, violent turns are going to contain a broad spectrum of frequencies) to give the largest response. so

*maybe*you can construct some kind of 3d model of the car in terms of damped harmonic oscillators, look at what the fundamental modes are for that system, find the most likely candidates, and calculate some kind of response at those frequencies.it's such a complex problem i don't see a simple approximation. but maybe something simple and obvious will come out once you start pulling it apart.

tbh i find the whole approach odd. who quoted for this? maybe they had an idea of what to do?

it might be better - if you have the data - to just fit some kind of model to existing data, without trying to understand the physics in any detail (think neural nets). but that is likely ging to need more data than you have. perhaps there is some half-way point where you do a crude analysis of the physics to give a model that is then fitted to existing data...

or ask some smart physics students. smarter then me at any rate.

posted by andrewcooke at 5:19 AM on April 28, 2016

maybe you could get some physics simulation code, throw together a fairly simple "block model" of a car, and simulate the test at different speeds? by playing with the parameters you might get a feel for which components are critical, fit a crude curve to the envelope of allowed values, and stick that in your spreadsheet?

ps i actually have a friend (in chile, so maybe not expensive) who has done maths / physics consulting (largely for mining companies) including some work in australia. he might be interested in this, if you have a budget! (he's head of some dept in the u of chile).

posted by andrewcooke at 5:27 AM on April 28, 2016

ps i actually have a friend (in chile, so maybe not expensive) who has done maths / physics consulting (largely for mining companies) including some work in australia. he might be interested in this, if you have a budget! (he's head of some dept in the u of chile).

posted by andrewcooke at 5:27 AM on April 28, 2016

*they can use to have a*

**high level of confidence**that the test will be safe before they leave the workshop.**i don't know how to do that**.These two statements are in opposition. If someone's life is on the line based on these calculations, don't try to figure it out using the internet, outsource it to someone that can do it with a high level of confidence. The test facility can likely refer you to someone.

posted by Candleman at 5:55 AM on April 28, 2016 [2 favorites]

Either don't accept the job, or subcontract it to a specialist, as Candleman says.

With only the context provided, it sounds like you would be practicing outside of your area of engineering expertise. That's unethical, and you could potentially lose your engineering license and/or get sued should something go wrong.

posted by Cecilia Rose at 7:33 AM on April 28, 2016 [1 favorite]

With only the context provided, it sounds like you would be practicing outside of your area of engineering expertise. That's unethical, and you could potentially lose your engineering license and/or get sued should something go wrong.

posted by Cecilia Rose at 7:33 AM on April 28, 2016 [1 favorite]

Anything involving safety should be done by someone who knows what they are doing.

There is a book!

If you know the masses and centroids of the before/after vehicle you should get an idea of how much mitigation is required to offset the changes. If mitigation has not been done or is off by a significant fraction you have your "no" answer right there. If the answer comes back as "yes" then I would start finding a PE with automotive dynamics experience.

That gives your employer an inexpensive way to see if they need to back to the drawing board and a warning if they decide to go forward.

posted by pdoege at 9:50 AM on April 28, 2016 [1 favorite]

There is a book!

If you know the masses and centroids of the before/after vehicle you should get an idea of how much mitigation is required to offset the changes. If mitigation has not been done or is off by a significant fraction you have your "no" answer right there. If the answer comes back as "yes" then I would start finding a PE with automotive dynamics experience.

That gives your employer an inexpensive way to see if they need to back to the drawing board and a warning if they decide to go forward.

posted by pdoege at 9:50 AM on April 28, 2016 [1 favorite]

*For initial use I was thinking that an assumed spring rate would be OK.*

Absolutely not. You might as well say 'I will just assume that any CoG change less than 10% is 'probably fine'. Spring rate is enormously important to how the vehicle will react to a steering input at speed. You cannot 'roughly model this with a spreadsheet' unless it is a massively complicated spreadsheet, which sounds like it is so far beyond your experience level to make the request ridiculous (by the company). There are vehicle simulation packages that can do this, but they are not necessarily cheap for a reason. This is a pretty damned complicated thing.

It sounds to me like the company wants a cheap, half assed 'solution' that they think will save them a but of money by being a bit convincing. They will not, by any means, be able to 'knock something up' to do anything remotely accurate.

*come up with a spreadsheet or similar that they can use to have a high level of confidence that the test will be safe*

A 'high level of confidence' is not feasible or realistic given the method chosen. Anyone that tells you otherwise is flat out wrong. You can find an answer that the company may find convincing, but a 'high level of confidence' is not a genuinely possible result. You can probably come up with a ballpark guess, but absolutely no more.

You need to know the static geometry of the vehicle (ie suspension link lengths and relative paths through droop and compression) plus dynamic geometry (change in camber/caster/toe or bump steer through travel) for the expected suspension travel during the test (which means you need accurate spring and damping calculations to track suspension travel) and you will need to know this for the unmodified vehicle and post modification to track any sort of change in behaviour. You also need to know tyre stiffness (sidewall) and tyre pressures can drastically affect this, so you need to know what pressure the test would be run at.

There are means of doing this, and the only way to do it with any confidence is to do it properly. Get a decent suspension modelling software (there are lots around, but I don't use any so can't recommend one or know its limitations, although I know Adams is supposed to be very good at what it does). This is not at all as simple as 'as long as the CoG is below x% of the height of the roll centre we're ok'. You'll still be able to get it done for a fraction of a real world test, but there is a long way between not needing to do a $10,000 test and 'getting by with a $100 spreadsheet'.

posted by Brockles at 11:23 PM on April 29, 2016 [2 favorites]

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posted by russm at 7:23 PM on April 27, 2016