# Does more downforce affect the acceleration and top speed?

How can downforce make a race car faster, apart from being faster around corners? I just recently learned that downforce can help a car accelerate from 0-60 mph faster. Usually, I thought drag didn't have a great effect on a car's 0-60 time. I also thought that the more drag/downforce a car makes the slower its acceleration (at higher speeds) and top speed. Does a car make more downforce the faster it goes?

For example, a Lola B12/60 can go from 0-60 mph in 2.8 seconds and reach a speed of 206 mph with 725 hp, while the Peugeot 908 HDi can go to 60 in 3 seconds and reach a speed of 203 mph with 700 hp. Does this suggest that the B12 will make more downforce?

• In your question you have an unstated implication that downforce increases drag. Please clarify. Sep 7 '21 at 15:06
• "Does a car make more downforce the faster it goes?" - yes, the spoiler is like an upside down wing. Drag races and cornering are both traction limited, so for equal mass cars and excess engine power, downforce is the important first order factor. Although for cornering there is more complexity Sep 7 '21 at 19:52
• If I am not mistaken, wasn't the downdraft mostly affect the tail end of a car, therefore, it pushes the front end higher and effectively pushing the car forward as the center of forces shifts?
– r13
Sep 7 '21 at 19:54

You do not want to overcome the force of static friction when accelerating because that's when the dynamic friction takes over and your wheels slip. That means that the force applied on the edge of your wheel is limited by the static friction which limits how much effective torque you can apply to accelerate (or maintain speed while overcoming losses due to drag).

Downforce might not change the coefficient of friction but it changes the force of friction because it increases the normal force but does NOT increase the mass (inertia) which must be overcome to accelerate.

That means you can apply higher torque on your wheels before they start to slip which means you can accelerate faster (so long as your engine can provide said torque).

TL;DR: I will expand on DKNguyen answer, which provides all the salient points. i.e. (my interpretation) the downforce is desirable to provide a better interface/grip between the car and the ground.)

## Comparison of drag and lift coefficients for automobiles.

The following graph presents a comparison of drag and lift coefficients.

figure (source technicacuriosa

First of all notice the high value of drag $$C_D$$ on the prototype race car. You would expect it actually be lower than an average commercial car (It is not a spelling mistake!), and yet its over double.

Additionally, notice the value for the coefficient of lift $$C_L$$. Notice the negative value and fact that its an order of magnitude greater than a commercial vehicle.

*Short note on Lift on commercial (-non supercar-) vehicles: On of the reasons for the positive $$C_L$$, is the clearance below the vehicle. This makes the car loose grip and feel (sometimes) more like floating and become "wobbly" at high speeds (apologies the correct word doesn't spring to mind).

## Aerodynamic Drag and Engine

Although covered in many other answers recently the top speed is when the aerodynamic drag is equal to the force that ends up on the wheels when they are driven by the engine. I've written this long description, because the force on the wheels changes depending on the speed (assuming a constant power).

$$P= F\cdot u \rightarrow F= \frac{P}{u}$$

This is summed up very nicely in a graph like the following (notice that the $$\color{blue}{\text{blue curve}}$$ is depended on $$\frac{1}{u}$$ which explains the hyperbolic shape):

figure 2: Aerodynamic drag and force on the wheels (source: hogervorst)

The top speed is where the two curves meet.

## increasing the Power of the car (and the limitations)

Arguably, since its possible to increase the engine car, this would shift the $$\color{blue}{\text{blue curve}}$$ further up.

The problem is that as the $$\color{blue}{\text{blue curve}}$$ shift up, so does the Force at which there is equilibrium. And that force is the force that the wheel should be able to act on the ground. Therefore, there is a limitation based on the how much traction force is possible for the tires to exert.

## Traction force.

The traction force T can be approximated by the static friction law (not kinetic):

$$T = \mu \cdot N$$

Where:

• $$\mu$$ is the friction coefficient between the tires and ground (assume its constant)
• $$N$$ is the normal reaction to the ground. (Sometimes we forget that the normal reaction is not just weight.)

So this is where the Coefficient of lift comes into play. By increasing the coefficient of lift, effectively we can utilize better an engine with more horsepower.

Also keep in mind that the aerodynamic lift and drag have similar equations, i.e. :

$$F_D = \frac{C_D}{2}\rho\cdot A\cdot v^2 \qquad F_L = \frac{C_L}{2}\rho\cdot A\cdot v^2 \qquad$$

where:

• $$F_D$$ is the drag force
• $$F_L$$ is the lift force
• $$\rho$$ is the air density
• $$A$$ is the cross-sectional area
• $$u$$ is the velocity of the car

The point being, that: for a fixed surface/wing car increasing the drag has a proportional increase in lift (either upward or downward). The trick is to trim the car in such a way that optimises its performance.

## Bottom line

For the cars you are considering, the engine power is so much that you'd probably only burn rubber is not for a significantly high downforce.

So - in that high horsepower scenario - the downforce is desirable to provide a better interface/grip between the car and the ground. This can help to:

• improve handling (the car sticks to the ground)
• improve acceleration (provide better traction)
• increase the top speed by utilising better any overkill in horsepower (if trimmed correctly).

## Numerical Example

Assuming the values for the prototype car ($$C_D=0.75$$, $$C_D=-3$$), and $$\rho=1.225 \frac{kg}{m^2}$$ and $$A = 2 [m^2]$$, then the lift and drag values are presented in the graph below:

For 300 kph, (~ 185 mph), the downforce is about 30000 N. A car like that will between 7500 [N] and 15000 [N] so the normal reaction $$N$$, increases from $$m\cdot g$$ to respectively $$5\cdot m\cdot g$$ or $$3\cdot m\cdot g$$. This means that you can apply 3 to 5 times more force on the wheels.

Comparably, the drag will be twice that of a "normal" car, but there is still room to gain traction force.

You can see this in the diagram below, where 4 curves are plotted:

• the drag force
• the force on the tires from the engine for 247 hp
• the force on the tires from the engine for 741 hp
• the traction force limit (dashed line)
generic automobile prototype racing
$$C_L$$ 0.28 -3.0
$$C_d$$ 0.35 0.75
curves

In the case of the generic automobile the excess hp will never affect the top speed, because there will not be enough traction (at high speeds the lift will reduce the reaction from the ground and therefore the traction).

• Like throwing on more propeller blades even though it is less efficient because your warbird engine is so powerful. Sep 7 '21 at 16:33
• @DKNguyen I couldn't get the warbird reference. Could you explain? BTW, your answer was succinct and complete +1. Sep 7 '21 at 16:36
• Longer fewer blades are ideal for efficiency if it were not for material strength, ground clearance, and tip speed exceeding Mach 1. WW2 fighters have a lot of propeller blades when 1-3 blades is the optimum number, trading balancing for efficiency in that range. Beyond that there are few benefits but the engines were so powerful they used more blades so they could actually make use of that power to accelerate and go faster despite the increased propeller inefficiency of more profile and induced drag due to more blades. Sep 7 '21 at 16:50
• So the hp can affect the handling?
– user34865
Sep 7 '21 at 17:45
• @audiR8, it depends... I am not sure how to exactly interpret your comment. Could you elaborate on the reasoning behind that comment? Sep 7 '21 at 17:46

The downforce is needed to counter the lift. This will stick the rear end of the car back to the road and provide better traction and maneuverability.

Smart rear wings (they call them wing when they are high and spoiler when they are part of the body design) are designed to provide maximum downforce with minimum drag. This can be done by the correct angle of attack and adding defusers and spoilers. The units on the chars are pound-force.source