Steering Energy

[CWA]

Hi guys,

I'm trying to justify a target steering torque (at the wheel) for our car. I have found some initial torque values for typical FSAE cars (4-11Nm) from this source, which I'm sure is is trustworthy - http://www.formulastudent.de/a...ves-box-of-tricks/1/ (http://www.formulastudent.de/academy/pats-corner/advice-details/article/steves-box-of-tricks/1/). I'm also currently awaiting test data from a previous car which was fitted with a steering strain gauge. Instead of just copying these values, though, I would much rather calculate my own target, and use these previous values to verify what I have calculated is in the right ball-park.

I was hoping to do it through an approach that considers the "energy" required to steer a car with a certain steering torque value through an average lap. I would then use some human fitness data (if such data exists) that measures the energy certain people can output over a given time. This given time would of course be the typical time duration of the endurance event for one driver.

But I seem to be stumped at the first hurdle, how much energy is required to resist a steering torque. Classic mechanical 'work' is measured as a "force x distance". But what if you are applying a force without moving anything? For example, say you are doing lap after lap of skid-pad, a constant radius corner for say 10 turns. You are holding the wheel in a constant position, so applying a force, but the wheel is not moving a distance. Classical work theory suggests that you are not doing any work, and that no energy is transferred into the steering system. But as we all know, the driver is definitely using energy to create the force that is resisting the wheel. And the longer this force is resisted, the more energy is required from him/her.

And then there is of course the rate at which this steering torque can be applied, the speed that the wheel can be turned by the driver. This is what I initially considered to be steering "power", before actually thinking about it in terms of joules and work pretty much messed with my head.

Can anyone offer any advice as to this approach, is there something obvious I am forgetting? Has anyone every tried this approach before? If not, how have you other teams been setting your target operational steering torques?

Many thanks in advance,

Chris

[Owen Thomas]

You could probably look at it in terms of potential energy. If you also had steer angle sensors, you could translate that to the rack travel at any given angle. There's your Fxd. If you had both sensors hooked up at once you could probably find a few nice sweeps and make a pretty decent graph in no time at all.

[Dash]

Do the units really need to work out to equal energy? You could maybe say Force X Time and use that as a gauge. People get tired after a certain amount of time exerting force whether you are actually moving anything or not.

That said, I've found that if you just make the maximum angle for the wheels to be steered around +- 120ish degrees on the steering wheel and have a fairly low scrub raidus, the steering wheel torque isn't that bad. Our 2010 car was something like 90 degrees lock to lock and it wore the drivers out. After adding 0.5 inches to the steering arm on the upright, its a breeze. Our 2012 car uses steering as described above and I've driven it for hours on end without getting tired.

[MCoach]

Someone owes me a beer. http://fsae.com/groupee_common/emoticons/icon_razz.gif

Googled "formula sae steering system"

First link:

http://www.facepunch.com/showthread.php?t=970335

[CWA]

Thanks for the quick replies guys.

MCoach, thanks for posting that link up. I remember reading through it ages ago but I never saved it. I'm aware of how steering geometry effects steering torque, I just thought I'd go through the process the other way round, in seeing what value of torque I shouldn't exceed (based on driver performance), and consequently what geometry limits that gives me.

Owen, the problem seems to be the fact that rack displacement isn't really an indicator of the energy exerted by the driver. What you say about potential energy sounds interesting, could you go into any more detail on that idea?

Dash, I like the idea of not needing the units to match up. That idea would be good for measuring relative differences in steering geometry options. But ideally I would like to know what the actual energy exerted is in joules, so I could compare it to actual measures of human fitness, which I assume would also be in joules. Although, I haven't actually found any data like this yet, so it's likely I'll just be testing the driver's myself, and in that case i could use my own system of units..

EDIT - Oh, and I agree about what you said about the steering link on the upright, Dash. At the moment I am just trying to make that arm as large as can be packaged. We have a choice of a new steering rack this year, so I will then compensate by spec'ing the 'fastest' rack, to make up the overall ratio. By my calculations, the longer I can make the steering pivot, the less the forces in the toe arm will be (for a given torque around the steering axis from the tyre), so hopefully less toe compliance?

And it's interesting that you are implying scrub radius is the main factor that effects steering system torque. Did you mean castor trail? As I'm only aware that the scrub radius increases steering torque via it's contribution to diagonal weight transfer (also dependent on your castor/KPI) or if you have unbalanced longitudinal forces on the front wheels (a situation I haven't really considered in FS). In my mind, the mechanical trail will have a much greater effect on steering torque.

[BillCobb]

The proper way to balance your steering effort with vehicle response is to factor the steering gain (g/100 deg SWA at some designated speed) against the steering torque gradient (N-m/g). These are typically nonlinear functions because of tire properties, but you can compute a work function from the torque x angle response and take some derivatives. If you have power assisted steering, the situation becomes even more complicated. When you compute an average slope between +- a designated g level, you will capture the essence of the situation. If this 'work sensitivity' is high, that usually means the car is 'quick' and the corresponding effort is too low. If the 'work sensitivity' is low, the car is too 'slow' for the high amount of effort. Manual steering vehicles usually have a low work sensitivity (the car's gain is low because you need a high steering ratio to live with the high effort). Cars that are twitchy or nervous or whatever else the uninformed call them, have too much gain for the low effort response.

Yes there is an ideal balance, for which metrics are computed and vehicles designed around, that produces a steering feel that just about everybody in that segment will agree is just right. Sportier handling preference gets a higher numbered metric. Much of this is market segment driven in the prodution engineering world.

Its difficult to work with this relationship if you are stuck with manual steering, low tire aligning moments, high tire pressure, low caster or kingpin inclination angles, high or low vehicle understeer, tires too big for the car weight, and the list goes on. Meanwhile you also have the low speed effort situation to deal with in which tire scrub torque plays a part.

But there is a lot of merit to your challenge. If the driver can not control the car because of high or low gain or effort in all speeds of the course, you have not done your job.

[Owen Thomas]

Owen, the problem seems to be the fact that rack displacement isn't really an indicator of the energy exerted by the driver. What you say about potential energy sounds interesting, could you go into any more detail on that idea?
Basically, take your strain data and convert it into a torque (s=E*e, etcetera), then divide by pinion radius to get a force. Use steer angle and the mechanical ratio of your steering rack to convert degrees of steer into linear rack displacement. Alternatively, just use the equation E = Tau*angle to get energy. Do it all in excel, apply the conversions to the data you are interested in, and plot force x displacement vs. time. You now have a graph of energy exerted over time.

Also of interest, if you look at some data from 0 deg to 45 deg, the area under a force vs. displacement graph will show how much energy it took to get to that point.

I think this will work nicely for you because you can look at specific scenarios as well as entire runs of data. By massaging the data a little bit, you can see exactly how much energy is exerted through something like an endurance run. Pretty neat!

Since you're dealing with real data, a lot of the non-linearities and difficult to explain factors are not really an issue (bonus!); however if you ever want to model it using theory you may have a tough time. Also, when you're looking at fitness data, you will probably see it in calories, not Joules. Shouldn't be a problem, but don't be thrown off by it.

[DougMilliken]

What BillCobb said.

Aircraft engineers have been looking at flying qualities in great detail, for a long time. Their methods are very well documented and are typically part of the specification for new aircraft. For example, tests have been performed with special aircraft where it is possible to vary the control force, motion and damping. Trained engineering test pilots repeat the same specific maneuvers with different control properties and the data is used to develop the specification.

This work depended on developing a suitable subjective rating technique and accompanying rating scale so that comments from different pilots could be compared. This is named after the main experimenters, the Cooper-Harper Rating Scale (overview on Wikipedia).

Further reading, if a bit daunting at 700 pages, is this former military spec, now converted to a "handbook": "FLYING QUALITIES OF PILOTED AIRCRAFT" MIL–STD–1797A. PDF copies are available for download.

[Dash]

Originally posted by CWA:
Thanks for the quick replies guys.

MCoach, thanks for posting that link up. I remember reading through it ages ago but I never saved it. I'm aware of how steering geometry effects steering torque, I just thought I'd go through the process the other way round, in seeing what value of torque I shouldn't exceed (based on driver performance), and consequently what geometry limits that gives me.

Owen, the problem seems to be the fact that rack displacement isn't really an indicator of the energy exerted by the driver. What you say about potential energy sounds interesting, could you go into any more detail on that idea?

Dash, I like the idea of not needing the units to match up. That idea would be good for measuring relative differences in steering geometry options. But ideally I would like to know what the actual energy exerted is in joules, so I could compare it to actual measures of human fitness, which I assume would also be in joules. Although, I haven't actually found any data like this yet, so it's likely I'll just be testing the driver's myself, and in that case i could use my own system of units..

EDIT - Oh, and I agree about what you said about the steering link on the upright, Dash. At the moment I am just trying to make that arm as large as can be packaged. We have a choice of a new steering rack this year, so I will then compensate by spec'ing the 'fastest' rack, to make up the overall ratio. By my calculations, the longer I can make the steering pivot, the less the forces in the toe arm will be (for a given torque around the steering axis from the tyre), so hopefully less toe compliance?

And it's interesting that you are implying scrub radius is the main factor that effects steering system torque. Did you mean castor trail? As I'm only aware that the scrub radius increases steering torque via it's contribution to diagonal weight transfer (also dependent on your castor/KPI) or if you have unbalanced longitudinal forces on the front wheels (a situation I haven't really considered in FS). In my mind, the mechanical trail will have a much greater effect on steering torque.

I'm not trying to imply anything. I would just say keep everything ( Castor, castor trail, kingpin, scrub, etc ) reasonable and it should work out. If you have RCVD, see pages 399-400. They talk about effects of steering axis geometry and steering wheel force. I'm sure there are other pages in the book to consult as well.