Understanding aeromaps for setting up ride height

When a racecar moves through the air, it generally experiences 3 main forces:

1. Drag: This is an aerodynamic resistance force against the vehicle's motion. It acts on the car's longitudinal axis and is determined by frontal area, air density, vehicle speed, vehicle shape and use of aero devices like wings, spoiler etc. It is denoted by the formula given below: D = 0.5*P*V^2*Cd*A where D = Drag force, P = air density, V = velocity of the car, Cd = Coefficient of Drag, A = Frontal area of the vehicle
2. Negative lift or Downforce: A Lift is an aerodynamic force that acts upward on a racecar. Negative lift is desirable for a race car as it increases the vertical load on tires and increases the tire's coefficient of friction (" vertical load and coefficient of friction on tires work in a different way known as tyre load sensitivity, we will talk about it in a different article"). Thus race cars need more negative lift or downforce to go through a corner in the quickest possible way. Downforce is calculated from the equation given below: L = 0.5*P*V^2*Cl*A where L = Lift force, P = air density, V = velocity of the car, Cl = Coefficient of lift, A = Frontal area of the vehicle
3. Side forces: This acts laterally on the vehicle influencing vehicle handling when lateral winds act on a car. In the motorsport environment, these forces are neglected because they don't affect race car setups and if it does there's nothing that an engineer can do about it.

All the three forces are better explained in the image below:

How drag and downforce affect race car setups?

Drag and downforce are related when setting up ride heights or wing angles of a car. Let's consider a car to be an aerofoil, the more rake angle a car will carry, the better downforce it will generate. But each car limits on how much rake you can carry because of the design flaws. So rake is the angle formed between the car's floor or underbody with the track surface. Lower front ride height with higher rear ride height results in high rake angle. This can be better explained in the image shown below:

A higher rake (under the limits) gives better downforce but increases the overall drag of the car which affects top speed and acceleration during a race. Lower rake reduces the overall drag of the car but also reduces downforce which affects the cornering speed of the car. So tracks like Spain, Hungary, and Monaco require high downforce where high rake has utmost importance but in tracks like Monza (Italy) and Austria low rake plays a key role. But tracks like Spa (Belgium) and Silverstone (UK) require a good balance between drag and downforce. It means trying to get maximum downforce with the lowest possible drag. But wait is this possible? Drag and downforce are rivals to each other isn't it?

Race and performance engineers create aero maps to find out the perfect balance between drag and downforce.

What is an aeromap?

It's a graphical visualization of the relationship of different data like coefficient of drag, coefficient of lift, aerobalance %, aero efficiency etc. with different ride heights and wing angles. The behaviour of the car in response to various setup modifications is then predicted using these aeromaps. The ability to promptly comprehend and analyse the impact of various setup modifications is crucial when the driver, track, and conditions change, which is why aeromaps has grown to be such an important aspect of race engineering.

Creating an aeromap using MoTeC i2 and Excel

Let's create an aeromap for the BMW M4 GT3 in Asetto Corsa because I am not rich enough to buy a BMW and try it in real tracks. So sims are the closest thing we can use to learn stuff ("That's the reason I call sim racing as poor man's race car"). To create aero balance versus ride height sensitivity map, first we need to find front and rear aero loads. So following math channels are created based on formulas given below:

 Front_aero_load = MR_f*Spring_rate_f*{FL_susp+FR_susp}+{(M*Long_G*9.81*h_COG)/WB}         

• where MR_f = front motion ratio, Spring_rate_f = Front spring rate, FL_susp = front left suspension travel (from zeroth position), FR_susp = front right suspension travel (from zeroth position), M = mass of the vehicle, Long_G = Longitudinal Gforce, h_COG = height of centre of gravity, WB = Wheelbase

Rear_aero_load = MR_r*Spring_rate_r*{RL_susp+RR_susp}+{(M*Long_G*9.81*h_COG)/WB}         

• where MR_r = rear motion ratio, Spring_rate_r = rear spring rate, RL_susp = rear left suspension travel (from zeroth position), RR_susp = rear right suspension travel (from zeroth position), M = mass of the vehicle, Long_G = Longitudinal Gforce, h_COG = height of centre of gravity, WB = Wheelbase
• To find aerobalance percentage we can just use the calculation given below:

aerobalance(%) = {Front_aero_load/(Front_aero_load+Rear_aero_load)}*100        

We can use the above formulas with different ride heights to create an aeromap. But using these formulas in low-tier motorsport is quite tough (as I was working in one of the series). As we don't get car data, there are a lot of unknowns here like motion ratio or spring rate. These values change depending upon the stiffness of the springs or anti-roll car plus because of financial constraints, teams don't invest a lot in sensors. In low-tier motorsport, basic sensors are used like strain gauges for tire loads, accelerometers for calculating Gforces and Gps for speed and racing lines. Generally, aero maps are build using CFD tools but as we don't have car dimensions or car data, it is very difficult to run simulations. Then how do we create aeromaps ?? well I have thought of a workaround to create those maps. let's try it out. (P.S it's just an idea to throw out as we are engineers and we need to find the best ways to solve it with limited data)

Creating aero maps using tire load channels

Calculating tire loads without downforce:

So let's try a dragstrip test on the BMW M4 GT3 to make our aeromap. Recording tire loads of the car at 10km/hr (constant speed) with 0 degrees of steering input will give the front and rear load without involving aero. The image highlighted below shows the FR, FL, RL and RR loads at 7km/hr. Now averaging the tire load channels using statistical mean will give a fixed tire load at 7km/hr. This is the load without downforce.

To create averaged tire load channel at 7km/hr, you can use the math channel below:

stat_mean(choose('Corr Speed' [km/h]  >=  7 AND 'Corr Speed' [km/h] <=  10 AND 'CG Accel Longitudinal' [G]  == 0.1, 'Tire Load FL' [N], invalid()))        

Similarly, all fours tire loads can be averaged.

So, FL= 3411.90 N, FR= 3411.40 N, RL= 3414.09 N, RR= 3416.82 N

Calculating tire loads with downforce:

Now, lets run the car at 150 km/hr (constant speed) to record tire load involving downforce. Then averaging the tire loads using statistical mean to get fixed tire loads at 150 km/hr. The image highlighted below shows the FR, FL, RL and RR loads at 150km/hr.

To create averaged tire load channel at 150km/hr, you can use the math channel below:

stat_mean(choose('Corr Speed' [km/h]  >=  150  AND 'Corr Speed' [km/h] <=  152 AND 'CG Accel Longitudinal' [G]  == 0.1, 'Tire Load FL' [N], invalid()))        

Similarly, all fours tire loads can be averaged.

So, FL= 3861.33 N, FR= 3877.59 N, RL= 4301.15 N, RR= 4304.37 N

Let's use some simple mathematics:

Total front axle load without downforce = FL + FR = 3411.90 + 3411.40 = 6823.3

Total front axle load with downforce = FL + FR = 3861.33 + 3877.59 = 7,738.92

Front aero load = 7738.92 - 6823.3 = 915.62 N

Total rear axle load without downforce = RL + RR = 3414.09 + 3416.82 = 6,830.91

Total real axle load with downforce = RL + RR = 4301.15 + 4304.37 = 8,605.52

Rear aero load = 8,605.52 - 6,830.91 = 1,774.61 N

So final aero balance(%) = {Front aero load/(Front aero load + Rear aero load)}*100 = {915.62/(915.62 + 1774.61)}*100 = 34.03%

You can make Math channels for this or use Excel VBA to automate the calculation.

Using this method we can plot aero balance for each front and rear ride height measurement. We can automate the whole process using math channels. Image shown below gives an understanding of aero balance map vs ride height of the race car.

Creating Drag plot vs Ride height

As we know, the drag coefficient is very important for a race car because if we carry more rake or wing angle, we may be faster in corners but it will make us a lot slower in straights of a race track. As engineers, we need to find a perfect balance between drag and downforce. The goal is to have a suitable aero balance for the best grip with minimum drag. To create a drag plot, we need to do a coast-down test on the car. Coast down test is letting the car slow down itself without using braking force. To do that driver needs to engage the clutch at 150km/hr while keeping the foot off the brakes and accelerator. The car automatically slows down due to air drag(resistance). When the car slows down without engaging brakes, two forces are acting on the car. One is rolling friction which occurs at the tire-to-road contact patch and other is the aerodynamic drag.

To find coefficient of aerodynamic drag, we need to eliminate rolling drag. let's do some experiments. To calculate rolling friction, we need to do the coast-down test on the car at 30km/hr because at such a low speed no aerodynamic forces are acting on the car.

F(rolling drag) = M*Glong*9.81

where M = mass of the car, Glong = longitudinal acceleration due to gravity

To create a math channel:

stat_mean(choose('Clutch Pos' [%]==0 AND 'Throttle Pos' [%] ==0  AND 'Brake Pos' [%]==0 AND 'Corr Speed' [km/h] >= 10 AND 'Corr Speed' [km/h]  <= 30, 1355*abs('CG Accel Longitudinal' [G])*9.81, invalid() ))        

We are taking statistical mean because we need to average values for rolling drag and brake and throttle position should be zeroed.

So the final results are shown below in the image below.

Now that we have isolated rolling drag, substracting it from overall drag will give us aerodynamic drag at 150 km/hr.

Aerodynamic drag = Overall drag - Rolling drag

Now,

F(aerodrag) = 0.5*Cd*A*P*V^2

Cd*A = {M*Glong*9.81 - F(rolling drag)}/(0.5*p*v^2)

where M = mass of the car, Glong = longitudinal acceleration due to gravity, p = air density, v= velocity

Following math channel for calculating Cd (coefficient of air drag):

stat_mean(choose('Clutch Pos' [%]==0 AND 'Throttle Pos' [%] ==0  AND 'Brake Pos' [%]==0 AND 'Corr Speed' [km/h] >= 75 AND 'Corr Speed' [km/h]  <= 152, ((1355*abs('CG Accel Longitudinal' [G])*9.81)-('Rolling Drag' [N]))/'Dynamic air pressure' [Pa], invalid() ))        

Hence, we got the coefficient of drag. Plotting against the ride height measurements will give us a CdA map.

Coefficient of lift versus ride height

This is something you can try yourself. The lift coefficient is used to calculate the overall downforce of the car which is the sum of the front load and rear load. I have given the formula below, you can automate the process using math channels or Excel VBA.

Cl*A = (Front aero load + Rear aero load)/(0.5*p*V^2)

where Cl = coefficient of lift, A = frontal area, p = air density and V = velocity

Final Results:

Using coast down and constant velocity test on the car in a dragstrip will give aero balance, drag coefficient and lift coefficient values. Everything can be done at one go where the car moves at a constant velocity of 10km/hr to find tire loads without downforce and accelerates to 30km/hr and then engages the clutch to decelerate to get rolling drag. After that again accelerating to 150km/hr, holding it at constant velocity and then engaging the clutch to decelerate to get aero drag.

Drawbacks of this method:

• Sometimes this method fails if the car has too much bump steer or if the coast down and the constant velocity test is done on bumpy track surfaces like Sebring.

Follow me for more articles on trackside engineering. Happy Racing!!