Intersecting extended steering arms at the rear axis result in 100% Ackermann….. or not?

With the high season of most Formula Student Competitions coming up soon, I would like to share a thought about a common misconception concerning Ackermann. I guess I do not have to elaborate on the principle of Ackermann, but I would like to elaborate on the way ‘100% Ackermann’ is being defined and established. During my previous years of judging in FS I have seen much incorrect information by some teams. There are several methods for calculating the Ackermann percentage, but here I'll show you the method that, in my opinion, provides the most insight.

First things first: 100% Ackermann is NOT achieved by intersecting the extensions of the steering arms at the rear axis as shown in Figure 1. There is not any mathematical / geometric evidence for this. It is an approximation of 100% Ackermann, but nothing more. To understand this, just look at the steering mechanism from a top view, and look at the geometry of the steering mechanism with all its variable dimensions. (position R&P relative to the front axis, the length of the steering arms, forward or rearward direction, the size of the steering rods relative to the R&P, etc).

To establish the % Ackermann, the engineer/designer has to make several choices:

1)     For which corner radius and what speed do you want to optimize your Ackermann?

2)     What are the characteristics (slipangles) of the tyres?

3)     Which % Ackermann matches the tyres with the corners?

The percentage Ackermann is a Design Objective which follows from the tyres you will be using (a.o. what slip angles can you expect), and from the racing track you would like to optimize the car for (for what corners do you want to optimize the car): there is a difference between slow, tight corners (a la Monaco) or real fast corners (like you see at Francorchamps). When you are the engineer, YOU decide!

Figure 2 shows the 100% Ackermann angle for a corner radius of your choice, which is angle F_left-M-F_right. Now it is up to you: which percentage Ackermann do you want? Again, I am not elaborating on your choice, but only on the way you can express your chosen percentage. Now have a look at Figure 3: whatever angle you choose, you express your actual choice as a percentage of this 100% angle.

At 100% Ackermann both front wheels are steering around point M. But if the wheels are steering around M’ the % Ackermann will be:

tan (δ_out) =     WB           =>   B =      WB      – Tr_front

                    (B + Tr_fr)                     Tan (δ_out)

And with  δ_{ins at 100% Ack}  = atan (WB / B) the % Ackermann can be written as:

% Ackermann =      δ_{ins, actual}    - δ_outs        * 100%

                              δ_{ins at 100% Ack} - δ_outs 

δ_outs                  : steered angle outer wheel

δ_{ins at 100 % Ack} : steered angle inner wheel at 100% Ackermann

δ_ins                     : actual steered angle inner wheel around M’

Now the steering geometry of your choice is expressed as the % of the theoretical 100% Ackermann angle. The outer wheel has the steered angle of your choice (with respect to the chosen corner radius), and the steered angle of the inner wheel dictates the chosen percentage.

Figure 4 shows the layouts if the different percentages Ackermann from positive to zero to negative. This graphic I made because I hope it provides you a great insight.

“Where are the slip angles?” I hear you thinking….  Two answers: There is a difference between the kinematic, static value and the dynamic value. Measuring Ackermann (by calculation or with the front wheels e.g. on turntables with a nonius scale) can only be done static. But of course you want to know the dynamic value, being the Ackermann geometry including the slip angles, and I assume that you know how to do that. And there is enough literature about this. E.g. in our book Race Car Handling Optimization page 171.

This all means that there will be a difference between the % Ackermann static and dynamic. Again: we look at the static one to be able to design and measure, and we look at the dynamic one to optimize the dynamics of the car.

The attentive reader will say that ‘B’ in the figures is not the corner radius. This is true indeed for a car at high speed producing slip angles in all four tyres, but at very low speed (at the parking lot) it is. The dynamic corner radius is the distance between the CG of the car and M or M’. The dimension ‘B’ is a static, geometric dimension.

The final question I put up here might generate some turbulence: how important is the Ackermann….? Well, hold your breath: a bad Ackermann can ruin your results (sometimes without the engineer realizing it!) but it will hardly guarantee that you will win races. Let me give you two real life examples:

During the years that I was active in a Renault Megane Cup, the first ten qualifiers were within 1 sec at the grid. So each 0,1 sec counted. Every event there was one guy who qualified at Saturday at the first row, but after the start on Sunday he dropped back to 4^th or 5^th, sometimes he finished 3^rd. A couple of years later one of his mechanics (an old student of mine) confessed to me that the driver qualified with illegal McPherson struts from which the steering arms were ‘modified’ to match the required Ackermann with the slicks which were used rather than the original McPheron strut matching the street tyres. Saturday night the Renault paddock was one big party ground, and nobody noticed that the mechanics were replacing the illegal struts with the legal struts, such that he was legal for the race on Sunday. Conclusion: the proper Ackermann delivered a few 0,1’s of a second, but in spite of this, the driver never achieved pole. (I wasn’t angry when I heard this, actually I admired their clever creativity!).

The second example is that from a tyre engineer I know well, who used to be active in absolute top ranks, but who actually didn’t care much about what the designer had in mind concerning the % Ackermann. Still they won races and even WC’s….!

In other words: with two equal drivers in equal cars during qualifying Ackermann can make a difference, and since FS is an individual effort (no wheel banging with other cars!) a proper Ackermann can make a difference indeed. But if your car is 3 secs off the pace, there might be other odd variables with much higher priorities!

Whatever you decide to choose concerning the % Ackermann, be sure you fully understand what you are doing, and even better, be sure that you can explain it – including the proper % Ackermann calculation! – correct to the jury! 

Do not show up with a picture like in Figure 1 ever again…!  😉

This is Blog nr 3 in a series of blogs concerning vehicle dynamics of race cars by Ton Serné.

They are based on the book ‘Race Car Handling Optimization’ 2^nd ed. (ISBN 978-3-658-47190-3), see www.handlingracingcars.com .