GPS Unit for Formula SAE Car

[Reed Sullivan]

My name is Reed Sullivan, I am on the University of Michigan Formula SAE Team, MRacing: http://mracing.engin.umich.edu

We are looking for a GPS unit with multiple antennas to calculate body slip angle, match gg diagrams with position maps, help out with driver training, etc.

We are willing to pay for one, but a donated system someone has upgraded from would be preferred. Any unit donated could be written off as a tax deduction and possible sponsorship benefits could apply to any company or individual (have your name or company on the car). We compete each year in the country and in Germany and we are currently ranked first in the world, so any company name on the car will not go unnoticed.

We are still looking into our options so any help or advice would be much appreciated.

Thanks in advance.

Best Regards,
Reed Sullivan
rsully@umich.edu

[NPalacioM3]

My name is Reed Sullivan, I am on the University of Michigan Formula SAE Team, MRacing: http://mracing.engin.umich.edu

We are looking for a GPS unit with multiple antennas to calculate body slip angle, match gg diagrams with position maps, help out with driver training, etc.

We are willing to pay for one, but a donated system someone has upgraded from would be preferred. Any unit donated could be written off as a tax deduction and possible sponsorship benefits could apply to any company or individual (have your name or company on the car). We compete each year in the country and in Germany and we are currently ranked first in the world, so any company name on the car will not go unnoticed.

We are still looking into our options so any help or advice would be much appreciated.

Thanks in advance.

Best Regards,
Reed Sullivan
rsully@umich.edu

I wish I had something for you, Reed!

Someone help the young man out, great kid!

[Neil_Roberts]

GPS is just not accurate enough to measure slip angle. It wouldn't be hard or expensive to create a direct yaw angle sensor from a castering wheel with a potentiometer mounted to it. Of course there are also fancier ways, like this.

[Reed Sullivan]

Thanks Nick and Neil!

I do like the castering wheel idea. Very interesting. I would just be worried about a spin out over extending or breaking the potentiometer. Also, would the castering wheel need to have some kind of suspension since you would not want it to take on any load over bumps or be too light for stability reasons? But, you already don't have a linear potentiometer path and suspension travel would make it even worse to convert the pot data to a castering wheel angle. We have pretty sub-par damper pots so I'd be worried about any conversions there.

But for accuracy's sake, I feel like the multiple antennas we want should give us the desired accuracy especially since they can be spaced out a reasonable distance.

If the GPS ended up not being accurate enough, there are many other things we would use the GPS data for.

Thanks
Reed

[Neil_Roberts]

I do like the castering wheel idea. Very interesting. I would just be worried about a spin out over extending or breaking the potentiometer.

Hard travel stops?

Also, would the castering wheel need to have some kind of suspension?

Yes. Think simple.

But for accuracy's sake, I feel like the multiple antennas we want should give us the desired accuracy especially since they can be spaced out a reasonable distance.

Some of the accuracy claims for GPS heading measurement are somewhat hard for me to believe. An easy experiment to perform would be to compare position and drift of two GPS units on opposite ends of a table.

[2BWise]

VBox sells a unit that puts to use two GPS antennas and will calculate body slip angle. With how short an SAE car is though I'm not sure if you'd be able to get enough distance between the two to get the accuracy you're looking for. Also, with how tight the courses are I would think you'd end up within the deadband of the gps signal/drift. What you could do is use a yaw rate sensor to measure actual yaw rate and create a math channel that calculates a yaw rate based on speed and ay. You can then compare these two values with the difference (integrated difference) relating to the body slip angle. Although, if you're looking purely at driver training and you got inexperienced drivers this may end up beyond their ability to utilize. There are OEM sensors available, but their output is over CAN. If you've got a CAN network on the car you've then got a simple solution.

[924RACR]

Although, if you're looking purely at driver training and you got inexperienced drivers this may end up beyond their ability to utilize. There are OEM sensors available, but their output is over CAN. If you've got a CAN network on the car you've then got a simple solution.

This.

Actually, there are analog OEM yaw rate sensors... just older than you're used to, Bill I have one in my 924.

But yeah, I think it'd be a waste of effort. Not to mention you'd need a person dedicated to data analysis and driver coaching... who, pretty much by default, needs to be pretty experienced themselves. And you'll need plenty of seat time availability.

I'd recommend sticking to the simpler stuff that'll be available off the shelf. If you're really dying to add sensors, make sure you have steering angle and throttle position sensors, in addition to g's and speed. That'll be enough to keep you busy until the competition.

[Reed Sullivan]

We have pretty experienced drivers for the series. We both raced in SCCA and are used to learning off of our own driver data. Not to mention how good it would be if we could relate all of our data to a track position and compare driver to driver.

I understand you can get that with accelerometer data and speed but in order to validate the vehicle model we are working on, we think GPS is the way to go. We have a person dedicated to data analysis as well.

We already have a decent set of sensors. We have steering position, steering torque, throttle position, brake pressures, wheel speed for each wheel, damper pots, and a few others. I believe we have already budgeted out a yaw rate sensor for this coming car.

We also put about 2000km on our cars each year. We start testing in mid-March. And although some of the things we want to use the GPS for aren't crucial, we are students so we want to learn and verify the modeling/designing we have done for the car.

[mousecatcher]

GPS is just not accurate enough to measure slip angle.

Yes it is. It's not GPS positional accuracy you need for slip angle, it's velocity measurement and for that purpose GPS is fine. I don't have my notes handy but IIRC GPS speed accuracy is good enough to know slip angle to within .1° at 50-ish MPH. For very slow speeds slip angle accuracy drops off quickly.

But you need two antennas and these things start at around $7500.

It wouldn't be hard or expensive to create a direct yaw angle sensor from a castering wheel with a potentiometer mounted to it. Of course there are also fancier ways, like this.

Yaw rate isn't good enough because of sensor bias. There's lots of literature on the subject.

One particular example is http://ieeexplore.ieee.org/xpl/freea...number=4529100 (sorry not a free download). I haven't studied that paper thoroughly but in the context of FSAE (where you have the car drawings) I think it's a good cheap approach.

[924RACR]

I'm guessing you mean sensor drift?

[mousecatcher]

Exactly. From the paper I linked:

Another way to estimate the vehicle slip angle is to use the kinematical relationship of slip angle velocity, yaw rate, lateral acceleration, longitudinal velocity and road bank angle.
...
However, it has been well documented in the literature that the kinematic method of slip angle estimation is prone to drift due to bias errors in the accelerometers and gyroscopes [2], [3], [9], [10], [12]. The estimated slip angle will drift over time no matter how small the bias is.

Attached is a graph from that paper showing error from this method with their test setup.

The references are:

[2] H. E. Tseng, D. Madau, B. Ashrafi, T. Brown, and D. Recker, “Technical challenges in the development of vehicle stability control system,” in Proc. IEEE Int. Conf. Control Appl., Aug. 1999, pp. 1660–1666.
[3] A. T. van Zanten, “Bosch ESP systems: 5 Years of experience,” in Proc. SAE Automotive Dynamics and Stability Conf., Troy, MI, May 2000, 2000-01-1633.
[9] J. Farrelly and P. Wellstead, “Estimation of vehicle lateral velocity,” in Proc. IEEE Int. Conf. Control Appl., Dearborn, MI, Sep. 1996, pp. 552–557.
[10] A. Hac and M. D. Simpson, “Estimation of vehicle side slip angle and yaw rate,” in Proc. SAE, 2000, p. 1, 2000-10-0696.
[12] C. Liu and H. Peng, “A state and parameter identification scheme for linearly parameterized systems,” ASME J. Dynam. Syst., Meas. Control, vol. 120, no. 4, pp. 524–528, Dec. 1998.

Perhaps that's not the whole story though, since vbox has a low end product ($1000) with a single GPS antenna, called driftbox, which measures "Drift Angle". Not sure how that equates to slip angle or how accurate it claims to be. Certainly for drifting you probably care about 3-5° increments of drift, whereas we care about .1-.5° of slip.

[na94]

I was going to say pretty much the same thin Neil said - I am building logging software for solosport that is gps-based, and while good enough to tell you who went faster and where, there is a real lack of accuracy to do what you want.

Would it be crazy to mount reference markers on your car and have someone video the run from a known height and angle, then pick up the markers in some form of 3d kinematic software? It might be the cheapest way to test different speeds and corner radii, no?

[924RACR]

0.1 deg of slip angle?!? You care about that???

I have trouble even imagining caring about even half a degree of slip angle... even on a formula car... 3 deg would seem adequate - though 5 deg resolution would certainly be pushing it...

This all sounds rather much like getting lost in the details... just because you can measure it, doesn't mean it's meaningful...

[nulrich]

What data acquisition system are you using? The GPS receivers are cheap, even ones good enough to measure slip angle, it's the rest of the system that costs money.

Nathan

[na94]

GP data intentionally has errors injected into it, and the errors do change, up to 1m.

If you are testing in a local area you can use a fixed ground station to determine the error amount, and transmit the delta to the onboard logger or use it to create maths channels after downloading the data. Apparently that can get you quite close.

[mousecatcher]

GP data intentionally has errors injected into it, and the errors do change, up to 1m.

If you are testing in a local area you can use a fixed ground station to determine the error amount, and transmit the delta to the onboard logger or use it to create maths channels after downloading the data. Apparently that can get you quite close.

Again, here you're talking about positional accuracy whereas for slip angle measurement you just need velocity accuracy; ground stations don't improve on velocity measurements. GPS can measure to within 1MPH and maybe to within .5MPH. http://www.ncbi.nlm.nih.gov/pubmed/15519597

I'll dig out my notes tonight on what kind of accuracy you actually need for reasonable slip angle numbers.

[mousecatcher]

0.1 deg of slip angle?!? You care about that???

I have trouble even imagining caring about even half a degree of slip angle... even on a formula car... 3 deg would seem adequate - though 5 deg resolution would certainly be pushing it...

This all sounds rather much like getting lost in the details... just because you can measure it, doesn't mean it's meaningful...

Maybe not .1° but certainly you care about 1° (and should therefore probably measure to 0.5°). I can't see slip angle being useful for driver training; yaw acceleration and yaw rate should be enough for that. So for the useful application of slip angle data -- simulation and evaluation against the tire model -- you want pretty good numbers.

5° is certainly not enough resolution; a radial tire is going to be at optimum grip around 5-8°. Of course that's tire slip angle and not CG slip angle. For equipment under $50k we're "only" measuring CG slip angle.

[Reed Sullivan]

Thanks a lot for all of your help!

We are looking for slip angle data for our simulation work and position for driver training. We talked about setting up a fixed ground station for the position. But, if you don't have an accurate position vector, what are you comparing your velocities to? I feel like that could be thrown off if your position is drifting. Am I wrong? If you had accurate yaw rate data and the velocity vectors, then could you get a slip angle measurement?

nulrich, we are using a Bosch ECU, data logger, and data acquisition software.

[na94]

Again, here you're talking about positional accuracy whereas for slip angle measurement you just need velocity accuracy; ground stations don't improve on velocity measurements. GPS can measure to within 1MPH and maybe to within .5MPH. http://www.ncbi.nlm.nih.gov/pubmed/15519597

I'll dig out my notes tonight on what kind of accuracy you actually need for reasonable slip angle numbers.

Why use the gps velocity when you can remove the positional error and calculate velocity yourself?

[Tiago Santos]

Reed, my understanding is that while GPS drift can change even within the same on track session, it's constant enough that velocity calculations will be accurate.. Meaning, whatever offset the GPS position has from the "real" position, it doesn't change fast enough to affect the speed measurements.

Does that make sense?.. The more I read it, the less sense it makes haha.

[mousecatcher]

Why use the gps velocity when you can remove the positional error and calculate velocity yourself?

Two reasons.

1. It's "hard" to correct positional error, especially in the Z direction.
2. Deriving the velocity by differentiating position is not as accurate as just taking the velocity directly.

GPS velocity is taken by doppler shift, not by comparing two GPS positions at two points in time. So, you don't even need a good GPS fix. Entry-level data systems still generally want a good fix because most of them use the GPS as a lap beacon as well as for speed.

[mousecatcher]

Reed, my understanding is that while GPS drift can change even within the same on track session, it's constant enough that velocity calculations will be accurate.. Meaning, whatever offset the GPS position has from the "real" position, it doesn't change fast enough to affect the speed measurements.

Does that make sense?.. The more I read it, the less sense it makes haha.

That's true, for systems that differentiate position.

[mousecatcher]

If you had accurate yaw rate data and the velocity vectors, then could you get a slip angle measurement?

Yes. You also need to know the road bank angle and pitch, which you can determine from accelerometers.

The problem is getting good yaw rate data. All of the literature I've seen says this is hard.

[Rick Ross]

It has been my experience that the 5 Hz GPS systems which are common in club racing provide a poor resolution speed trace in areas of high deceleration (for example, threshold braking from 140 mph to 40 mph in an FA/FB type car). If one compares the GPS speed trace to measured wheel speeds in such a braking zone, the correlation is not that great. This becomes even more of a problem when your data system determines longitudinal accleration by differentiating the GPS speed. I suspect that a 20 Hz GPS receiver would mitigate or eliminate this problem, but I have not yet seen any data obtained with a 20 Hz system.

When you guys refer to "CG slip angle" in the above posts, are you refering to the angle between the velocity vector and the car longitudinal axis? I am more familiar with the use of the term "slip angle" in the context of tire dynamics and modeling.

[mousecatcher]

It has been my experience that the 5 Hz GPS systems which are common in club racing provide a poor resolution speed trace in areas of high deceleration (for example, threshold braking from 140 mph to 40 mph in an FA/FB type car). If one compares the GPS speed trace to measured wheel speeds in such a braking zone, the correlation is not that great.

I'm sure part of that (correlation error) is due to GPS and sampling rate (5 Hz is awful slow), but part is also going to be due to rolling radius changing; the wheel speed sensor will always be wrong for "significant" changes in rolling radius. My point is, both traces are wrong, and both traces will have variable error rates.

When you guys refer to "CG slip angle" in the above posts, are you refering to the angle between the velocity vector and the car longitudinal axis?

Yes. Maybe "CG" isn't the proper prefix. But you're right, it's important to realize it isn't the tire slip angle. I'm sure with K&C data (?), steered angle, and front and rear accelerometers you could use CG slip angle to figure out tire slip angle. Maybe.

[mousecatcher]

So, for a Vx of 100 kph (62mph), a 0.2° slip angle gives us

Vy = 0.34 kph (= 0.2 mph).

Most google-able research seem to claim about 0.5 mph accuracy for GPS speed via doppler over a 1s interval. Vbox (VB20SL) claims to have a 0.1kph accuracy over 0.2s. If we are to take Vbox's claim with a grain of salt, and figure 1kph (10x worse) accuracy, we can roughly measure within 0.6° CG slip angle at 100 kph.

[Reed Sullivan]

Wow thanks for all the detailed information. Good stuff!

Since we know every aspect of our suspension geometry, we were going to use body slip angle to find the slip angle. We have sensors for all of the other necessary data.

[Rick Ross]

I'll need to verify this, but I am pretty sure that slip angles can be determined using single-axis lateral accelerometers located at each end of the car, assuming that you know the car's polar moment of inertia. Lateral velocities at each end of the car are determined by integrating the lateral acceleration channels, and yaw rate can be calculated if the polar moment is known. If this is correct you would not need a yaw rate sensor or a GPS receiver. And I suspect that two decent lateral accelerometers would cost less than a dual antennae GPS system like the VBox.

[924RACR]

I can't see slip angle being useful for driver training; yaw acceleration and yaw rate should be enough for that.

Agreed, definitely.

5° is certainly not enough resolution; a radial tire is going to be at optimum grip around 5-8°. Of course that's tire slip angle and not CG slip angle. For equipment under $50k we're "only" measuring CG slip angle.

This gets to the heart of our confusion/disagreement... we've been talking about body, or CG, slip angle - you're thinking of tire slip angle - and on that basis, yes, I'd agree, you'd want to know at least within 1deg, if not better.

[mousecatcher]

What is the CG slip angle of a car in a constant radius corner (skidpad) with neutral steer?

[924RACR]

IIRC that'll depend on the speed and radius...

[mousecatcher]

Well sure. The answer can be in terms of r and ω.

[George Main]

I'll need to verify this, but I am pretty sure that slip angles can be determined using single-axis lateral accelerometers located at each end of the car, assuming that you know the car's polar moment of inertia. Lateral velocities at each end of the car are determined by integrating the lateral acceleration channels, and yaw rate can be calculated if the polar moment is known. If this is correct you would not need a yaw rate sensor or a GPS receiver. And I suspect that two decent lateral accelerometers would cost less than a dual antennae GPS system like the VBox.

This is current use in F1 and Indycar. The accelerometer is placed at the axle center of the front/rear axle line (lateral line through axles) on the chassis center of this axis. Sampling rate is at 100+ samples per second. A third accelerometer (3 axis) is in use at the car's CG. Comparison of the three Accelerometer's signals can measure differences in G's for the axle planes by way of comparison. However extracting an absolute number for slip is difficult just using these sensors. (BTW, many also use a yaw sensor in the car's center as well to measure the point of rotation of the car)
The more accurate solution is a much more expensive one, using optical sensors (one pointed at each wheel) which measure the lateral acceleration movement of the ground vs the heading of the car and are pointed at the sidewall/contact area of the tire. The above mentioned (Accelerometer) sensors are used with the optical ones. As are laser ride height/suspension position sensors
Big strides have also been made in internal tire air pressure/temp sensing as sensors can now measure side wall and internal carcass temp in multiple areas with one sensor location. This also can be used to calculate tire deflection with pressure differences and side wall/contact patch info.
The GPS solution is also a very expensive one, as the accuracy needed Requires an "in the track" location beacon and two 20hz GPS units and antennas to gain 3-6mm (depending on the type of GPS UNIT) accuracy for comparing the heading of each GPS unit. Use of anything lower in HZ and without the beacon is simply inaccurate to judge even the driver's line let alone differences in .3 degrees of heading.
Laptime and speed are useful however but that's it for the lower number GPS units. Even the GPS G's number (measured from a satellite) is a subjective number and not a replacement for "on-the-car measurement".

Too add, as Reed mentioned they had a simulation program. Depending on the program's ability, accurate tire data (data drawn from "rolling tire machines") measuring deflection, pressure change, slip angle, spring rate, etc. and plugging that info into the sim program is extremely helpful. I know Adams has this ability.

Most of what's mentioned here is very expensive and there's no "cheap" solution for accuracy of a tire's behavior or the slip angle number, maybe someday we'll get a solution that costs a couple of hundred bucks instead of hundreds of thousands of dollars to accurately measure a rolling pneumatic rubber band.. IMHO.