Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/17/84; site twitch.UUCP Path: utzoo!watmath!clyde!cbosgd!ihnp4!houxm!twitch!guido From: guido@twitch.UUCP ( G.Bertocci) Newsgroups: net.auto Subject: Stiff vs soft suspension myths Message-ID: <191@twitch.UUCP> Date: Tue, 21-May-85 09:18:17 EDT Article-I.D.: twitch.191 Posted: Tue May 21 09:18:17 1985 Date-Received: Wed, 22-May-85 01:47:12 EDT Distribution: net Organization: AT&T Bell Labs, Holmdel Lines: 185 I have been intensely amused at the incredible number of misconceptions that have been posted in netnews and printed in the general media on how suspensions work. These articles come from everyone including so called authorities such as Car & Driver, Road & Track, BMW Roundel, and advertisers for suspension products. These articles often completely contradict each other. One of the favorite suspension myths is the so called "weight transfer" theory as a function of "stiff" or "soft" suspensions. THE "WEIGHT TRANSFER" THEORY IS TOTALLY BOGUS. I will prove that it is false. I will simplify the discussion with several assumptions and simplifications. 1. The auto in question does not change mass during cornering, or braking, or accelerating (forget about fuel and tire wear and relativistic effects). 2. It is easier to solve the problem for a steady state solution so the car in question is circling a flat skidpad of a fixed radius at a constant speed. 3. I will draw the dynamics for the front suspension only, (it is easier to do 2D drawings than 3D). The identical arguments can be made for the car as a whole. Remembering freshman physics, the entire situation can be represented with ONE point, CM - center of mass, However, it is useful to have several additional reference points, LT - left tire, RT - right tire. AR - axis of rotation around which the CM rolls during cornering. (Coming out perpendicular to screen at about the level of the subframe of a car, or slightly lower than the center of the wheels). FmT | v CM - center of mass X <-FcT AR FmL ---- FmR | | v v LT <-FcL RT <-FcR At each point we can represent all forces with a horizontal and a vertical vector. FmT - total force down due to mass of car FmL - force down measured at left tire FmR - force down measured at right tire FcT - total sideways force due to centripetal acceleration of car (cornering) FcL - sideways force at left tire FcR - sideways force at right tire In addition: FmT = FmL + FmR = constant (car does not change mass) FcT = FcL + FcR FcT is completely defined by V*V/R where V is velocity and R is the radius of the turn The entire problem can be represented with forces at CM, however, what we really want to know is what is happening at LT and RT, and in particular FmL and FmR. For any given speed around a skidpad, FmT and FcT are constant. For ANY suspension, if we know the angles and lengths of sides of the triangle, (CM,LT,and RT) it is simple geometry to compute FmL, and FmR. During straight line driving FcT = 0, and FmL = FmR = 1/2FmT. During cornering the change in FmL will be identically = -FmR, and the change can be computed by knowing where the CM is relative to the tires using simple geometry and FcT. There is NO WAY one can transfer weight from left tire to right tire or anywhere else unless one moves the CM. As a matter of fact, there isn't anyway to transfer weight anywhere, either with springs, sway bars, or spaghetti. Does the CM move during cornering? Some, but not very much. The CM does not move up or down (Unless they are so soft they bottom out). A car rides on springs that obey Hooke's law. (Forget about progressive springs, expecially since they tend to raise the CM during cornering). Since we have shown that FmL = -FmR, then by Hooke's law, the left side of the car will move down by the same amount that the right side moves up. (On progressive springs, the left side would move down less than the right side would move up, therefore RAISING the CM which deteriorates cornering ability.) The CM does move side to side slightly. If the CM were situated directly on the AR (axis of rotation) then it wouldn't move side to side either, however, the CM is usually slightly higher that the AR. Now for some numbers as to how much things really move. Let's pick some extremes. Some of you have probably seen the advertisement for Koni kits with a Camaro that looks like it is about to flip over, and then with it perfectly flat. The Camaro has between 7-8 degrees of body roll. The second photo is a phony since the car isn't moving as fast. If you look at pictures of race cars such as Ray Kormans BMW, Corvettes, or other cars with extremely stiff suspensions one will find that about the best a road car can do is 2-3 degrees. (Ignore Gran Prix cars). (You will get 1 degree simply from tire deflection, and bushings compressing). Pick an average car with a front wheel track of about 60 inches and a CM of 20 inches and a AR of about 10 inches from the road. With 7 degrees of roll the CM will move sideways 1.23 inches, while with 3 degrees the CM will move .52 inches a whopping difference of .7 inches! It turns out that the CM is usually lower which makes the difference even smaller. Using geometry, the car with 3 degrees of roll will enjoy an advantage of 2 percent in the loading of the outside tire over the one with 7 degrees of roll. Since the cornering force is more or less a function of the weight on a tire a generous assumption that 2% translates to an increase of 2% in cornering means that a your car goes from .800g's to .816g's on a skidpad. (The actual effect would be much less.) Since acceleration is the square of the velocity, if you were able to corner at 60.0 mph then you would be able to do 60.6 mph with your "rock" suspension. To reduce body roll from 7 degrees to 3 degrees, assuming 1 degree comes from tires and bushings, one must increase the effective spring rate (spring rate + sway bar) by 300%. For those of you, who drive BMW's, aftermarket stiff springs are advertised as 30% stiffer. Going from a 23mm sway bar to 25mm sway bar would increase the coefficient for the sway bar by about 20%. The point is that 300% is a hell of a lot stiffer than any normal individual is willing to tolerate, and therefore, going to a tolerably stiffer suspension is not even going to come close to the 2% we computed above. In conclusion, your springs, sway bars, cannot transfer weight anywhere, the best they can do is hold the CM stationary Even the difference between a racing suspension and a mushy suspension in terms of CM moving is maybe 2-3 %. People might be wondering just why do people want stiff suspensions anyway since weight transfer really isn't significant. The reason that they work is complex. Usually stiff suspensions are accompanied with a lower ride, which lowers the CM. In our example, lowering the CM from 20 to 19 inches decreases the load on the outside tire by 5.2% for any given turn. If the CM where at ground level the load on the inside and outside tire would always be 1/2 the weight of the car. Avoiding body roll is not so bad because of "weight transfer" but because it changes the suspension geometry, in particular camber. For example, a 2 degree change in camber will raise the inside of a 205 mm tire by 7 mm which will dramatically change the load pattern on a tire. By the way, all of this would be irrelevant if tires where linear devices. In other words if you doubled the load on a tire you would be able to generate twice sliding friction (Remember freshman physics). If tires worked that way, it wouldn't matter what you did. There is also an improvement during dynamics situations, (ie. a slalom) where the the car is not in a steady state. With a stiffer suspension, the chassis + body achieves a steady state position quicker, with less overshoot in body roll. One last note, that stiffer is only better on flat roads. As soon as you introduce any bump in the road, then one must deal with trying to maintain optimal tire contact with the road which is a 2nd order problem (the famous LCR circuits). The result is that there is a different optimal solution given amplitude of the road distortion and the spacing of the bumps and the speed of the car. Which means that you would really want a different suspension for each turn. And this is in addition to suspension geometry changes as a function of body roll and shock compression. Even on relatively smooth tracks, racing teams spend an incredible amount of time changing the suspension between different tracks. So to our friend who was worried about the softer Corvette suspension, I suggest that he not worry so much unless he wishes to spend to rest of his days going around a 300ft skidpad. The moral is that people tend to do the right thing for the wrong reason. Guido Bertocci P.S. Next week, I will give on a dissertation on the myth of "More rubber on the road with wide tires".