Vehicle Quasi-Statics 101: Testing Your Sim Model And /Or Your Car
This started life as a Word document so it kinda fell apart as it got pasted in here. Oops.
OK, to establish some facts on these cars amongst all the claims, noise, religion and trivial pursuits, I want to submit a few procedures that can be used to MEASURE some significant design parameters of them. These procedures have been used industry wide to evaluate vehicle performance relative to design intent. Believe it or not, vehicles today are designed around a set of constraints, goals and specifications that are flowed down into hardware, as opposed to slapping some metal, plastic and rubber pieces together, hoping for the best and changing parts and adjustment holes until you run out of time.
The first one is a simple but elegant way to measure the understeer of a car. The procedure has been called a Characteristic Speed Test or more simply a "C-Speed" test. That name used to be referenced when 'characteristic speed' was a favorite term. The Characteristic Speed is the speed of an understeering road vehicle at which the steering gain is 1/2 of the initial open loop gain. For the oversteering vehicle, there is a Critical Speed where, you guessed it, another factor with a 2 in it. The reason to know the approximate understeer of any vehicle is to gauge the sensitivity of steering and response bandwidth to variations and deviations in chassis, tire performance and operating speed parameters. Now I’m personally not a fan of using understeer/oversteer (tight or loose) because the metric doesn’t identify which end of the vehicle is at fault. In fact, you can ‘fix’ a vehicle in these conditions by manipulating the wrong end of the car.
This procedure could be, can and should be used on simulations of handling to determine recognized metrics indicating potential and real performance as well as parking lot tests with all the bells and whistles working on a real live car. It’s also just a great way to see what the laugh factor of your simulation is.
All you need is a yaw velocity or correct lateral acceleration signal and a forward speed signal, plus a tape measure to determine the wheelbase. You also need some way to hold the steering wheel fixed during each road test segment. We often used a seat belt pulled tight through the steering wheel rim to do this.
The test utilizes the notion that the decreasing, increasing or unchanging curvature of a vehicle path as speed (hence lateral acceleration) increases with a fixed steering wheel angle is a direct indication of its understeer or oversteer gradient.
In the good old days ('60's), a lunch box with a rate gyro and a fifth wheel were all that was needed to grab a car, head to a small test pad and get a plot on an analog paper sheet plotter to get a PFC measurement. The box had a built in analog multiplier to produce the lateral acceleration and a divider to produce curvature analog signals wired to the plotter. Even before that, a checker-boarded road and a movie camera were used to compute the speeds and yaw rates frame by frame. In the late '90's and 2000's, I used a VBOX to measure the two signals and reproduce values nearly identical to results from step, frequency response, and constant radius tests. Today, who knows what you guys will dream up.
The procedure is as follows. I’m focused on the road test. A simulated test is a no brainer. (At least I can imagine that).
Fix the steering wheel rigidly to the car body somehow and slowly and smoothly increase throttle until you reached a high lateral g level. Best to use a fixed transmission gear for automatic and manual cars for each data segment that can cover the desired range of g's without jerking the vehicle because of shifting.
Run the test as multiple segments covering several different fixed steer angles and both turn directions. Yes, this is how you can measure the understeer of a boat.
With the data piped into Matlab, Excel, Fortran, Basic or a calculator, you can finally get to the end of your search for the Holy Grail of your first New School Vehicle Dynamics report card.
I’ve attached two summary examples, one to show it works and the other to show what you might find out. Sometimes the truth is stranger than fiction.
First example is the use of a full blown nonlinear handling simulation throttled down to only a few linear constants which define a known, installed value of total vehicle understeer. I.e. I put into the simulation parameters that deliver the constant understeer response I want the data processing to deliver. I install specific values, turn the crank and compute the metrics I'm expecting from the simulation data. Yes, it works.
Next, I up the ante with generic FSAE car parameters (171 kg.) and add a few likely nonlinear effects (steering compliance and some nonlinear tire data with some forward TLLTD). You can see some of the effects of steering compliance and TLLTD effects in the plotted results. BTW, I'm not trying to deal out a full blown FSAE car because I don't (want to) know how much geometric and deflection steer you have, but you might want to know it.
Using both quasi-static simulation and road test results I'd bet we'd all want to see some results for a few sims (Danny ???) and some real track data (come on, cough it up). Once you have a tool like this, from simulation and road test, you will know exactly how to apply tuning and balancing changes to get a decent car. It should be obvious to you all that having a decent trustworthy and validated simulation cuts through all the lore and guesswork on the way to production of a really great vehicle.
Anybody got Game ? If some of you are still awake after contemplating this technique, I will post a vehicle DYNAMICS test procedure to make you really look and sound professional. Remember, the Human Factors aspect of vehicle design and specification is just as important as durability, etc.
Here's some data processing code in Matlab:
%% Constant Steer Increasing Speed Test: The C-Speed Test Bill Cobb Vehicle Dynamics 101
% Take out the trash: delete possible residue from previous activities:
clear all
% Get me some SIM or DAC data:
csmp_read % get simulation data
% Discard the startup transient if you have one:
inx = find(TIME > 1); % skip any blips.
URG = URG(inx); % yawrate * speed = ~ay(ss)
YAWVEL = YAWVEL(inx); % deg/sec
SPEED = SPEED(inx)*.277778; % Convert from km/hr to m/sec
L = L(inx); % Don't start sweating, this is a sim artifact to transmit the wheelbase parameter
% Turn the crank:
wb = L/1000; % convert wheelbase to meters
r = YAWVEL*pi/180; % convert yawrate to rad/sec
radius = SPEED./r; % computed turn radius
curvature = r./SPEED; % the math majors term for it
b = spap2(2,4,URG,curvature); % Spline fit. Use polynomial if you don’t have spline toolbox.
db = fnder(b); % derivative function
d = fnval(db,URG); % evaluate the derivative over the range
k = -wb.*d*180/pi; % understeer deg/g over the range
plot(URG,k,'r', 'LineWidth',2);
xlim([0 2.0]); ylim([-2 12])
xlabel('Steady State Lateral Acceleration (g)')
ylabel('Understeer (deg/g)')
supertitle(['Characteristic Speed Test Results']) % this function is from the Matlab Users Group.
title({[title2]},'Interpreter','none') % Use a title passed down from the sim
sidetext(['Bill Cobb zzvyb6@yahoo.com'],'Interpreter','none');
grid on
href(0)
vref(0)
legend('Installed Understeer in this vehicle is 3.0 deg/g') % comment only for this example
%legend('Understeer in this vehicle is from TLLTD and steer compliance')
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