# What limits the speed of a car?

From an engineering perspective, what limits the maximum speed you can reach with a regular car? I understand that some of the faster cars are for safety reasons limited to not run faster than say 250 km/h, but that's not my question.

I can think of several reasons, but not sure which of these is relevant:

1. Is the limit set by some part (which?) breaking if I increase the rpm, as suggested by red marks on rpm meters?
2. Or is it rather that you cannot get in fuel fast enough to keep increasing the rpm?
3. Or is it that friction/drag increases as you speed up and the engine cannot overcome this as it can only generate a maximum amount of force/torque? If yes, what does this amount of torque/force depend on?
• 250 km/h is "only" 155 mph. There are plenty of production cars that can go considerably faster than that. I have one. It's not a Bugatti Veyron (408 km/h), or even a Dodge Viper (332 km/h, stock), but she is fast. Going that fast is definitely not safe. Take it to a track. – David Hammen Jan 10 '18 at 3:03
• You accepted the wrong answer. There is no answer to this question in engineering. The answer lies in politics. This goes back to the 1970s, when there was pressure to impose speed limits on the autobahn. Mercedes, BMW and Audi (and later, Lexus) made an apparently successful bid to keep the autobahn unlimited by agreeing to electronically limit the top speed of their cars destined for Europe to 250 km/h speed limit. – David Hammen Jan 10 '18 at 13:50
• @DavidHammen Speed limiters are certainly the first thing you'll hit when trying to break the land speed record in a production vehicle, but I believe the OP is specifically wondering what else might limit the car's top speed. – Arnon Jan 10 '18 at 16:41
• @DavidHammen: I am specifically not interested in speed limiters. – user1583209 Jan 10 '18 at 19:53
• Engineering Explained: Why Has No Production Car Hit 300 MPH? – Digital Trauma Jan 10 '18 at 20:05

There are a few simple reasons why the speed of a vehicle (road conditions notwithstanding) may be limited:

1. Gearing -- Production vehicles with conventional transmissions have a limited number of gears. For most modern cars, this is usually 5 or 6, whereas older vehicles may have as few as 2 or 3. If the gear ratio of the highest gear is too low ("lower" gears are expressed as larger numerical ratios), it's entirely possible that the engine will redline before air resistance becomes a factor at all. This ties into your first point about the red zone on the tachometer. If you have reached redline, which is the maximum rotational speed of your engine, but don't have a higher gear to shift into, then you cannot go any faster without damaging your engine.

2. Drag -- Like any physical object, cars are subject to air resistance and other sources of drag (rolling resistance, etc). If the drag on the car exceeds the amount of power that the engine is capable of producing to the wheels, then your speed is once again limited.

3. Speed Limiters -- It's worth mentioning that production vehicles are almost always speed limited in the ECU (Engine Control Unit) for safety or legal reasons. If the ECU detects the wheels are spinning at a fast enough speed, it will cut power to the engine to prevent the vehicle from going faster. It's possible to circumvent this protection with an aftermarket ECU or with a modification to the stock one. As an example, some model years of the Honda Civic are speed-limited to around 120 mph (190 km/h).

4. Tire Ratings -- All tires have a certain speed rating, which is likely much less than the actual top speed of your vehicle. The speed rating is a single letter and is part of the tire code (see here for more information). For example, temporary spare tires may be limited to only 80 mph (130 km/h) before they are in imminent danger of suffering a blowout.

5. Stablity/Aerodynamics -- This is less of an engineering perspective than a practical one, but for a "regular" car there will be a certain point that the suspension and other components are not sufficient to keep the car driving straight down the road in a safe fashion. Anecdotal evidence to support this point comes in the form of a story about an old '70s full-size American car that, when taken up to triple-digit speeds, did not have the aerodynamic capabilities to keep the front wheels on the ground. In short, the lift from the air moving under the car lifted the front wheels off the ground into a terrifying high-speed "wheelie". Though this process did not technically cause the car to slow down, it certainly made it difficult to control at that speed.

• Tire ratings won’t stop a powerful car from going fast - just make it very unsafe.... – Solar Mike Jan 10 '18 at 7:36
• Aerodynamics is definitely engineering... – Solar Mike Jan 10 '18 at 9:18
• 1) is as far as I know not true for production cars in general. As a rule of thumb, they can reach top speed in 5th gear, and in 6th gear you can't go as fast because the drag grows faster than the engine power as a function of RPM. – Sanchises Jan 10 '18 at 11:27
• Regarding tire ratings, that's an issue also in aviation, and a limiting factor in overspeed landings of airplanes ("fixed-wing aircraft") which can lead to tire blow-outs, which in turn can lead to anything from a grumpy mechanic to, in extreme cases, a hull loss of the aircraft. – user Jan 10 '18 at 13:59
• In addition to this fine list, other factors include the roadway and other hazards. Racetracks are carefully prepared and cleaned surfaces. Everyday roads have rough pavement (sometimes potholes), are strewn with debris, and have curves engineered for vehicles going at a sane speed rather than 200+ kph. Low flying objects are also hazards. Birdstrikes are just as bad for fast moving cars as they are for airplanes. Even a large beetle hitting a "car" moving Mach 1 is probably a bad day. – David Hammen Jan 10 '18 at 22:00

So, what limits the speed is a combination of two things : the power from the engine with the gearing and the rolling and air resistance.

Up to approx 40mph the rolling resistance is the largest resistance, but above that speed air resistance is the dominant factor and increases the faster you go.

The engine power is fixed (ok tuning etc) but the gearing is also important - an engine of 200bhp can either power an agricultural tractor or a neat sports car.

Once the total resistance is equal to the power available at the wheels then you don’t go any faster.

• Now only does it increase the faster you go, the force increases quadratically and power cubically. Rolling force stays the same and rolling power increases linearly. So, go twice as fast, and your air resistance force is 4x bigger, whereas rolling resistance force is the same. Go 4x as fast, and your air resistance force is 16x, whereas rolling force is the same. So, if your car goes 160 mph, your rolling force is less than 6% of the total force. So, air resistance at high speeds is practically the only resistance. – juhist Jan 10 '18 at 19:20

Physics stops you. Ever ride a bicycle? 25 mph is easy, 30 is hard, 40 requres special gear or a very pumped up body, and 50 is nigh impossible. Why does the effort get so steep for such small speed increases? Air.

## Aerodynamic drag

Rolling resistance is the dominant factor when your car is going slow - that's why they're so hard to push. But at higher speeds, the ruling factor is aerodynamic drag. That's because rolling resistance is fairly linear. Aero drag is not, and is at least a second-order factor -- it comes on like a freight train at higher speeds. In fact I've heard coal trains that can do 40 mph loaded, can only do about 35 empty. That's because each empty coal car is a big scoop, catching the wind. And rolling resistance is close to nil for a train.

## Available power

Obviously, that aero drag is balanced against the power the engines can apply against it. They could get that empty coal train up to 70 mph if they put four times the locomotives on it.

You're talking about cars, so it's a matter of how much the batteries can supply and the motor-controller can push without taking damage. Or since you're assuming fuel-powered cars, it's about how much air the engine can move through. Adding the correct amount of fuel is easy. Airflow is decided by tuning - intake/exhaust ducting/porting/resonance, valve size and numbers, camming, stuff like that. (Also the engine redline (max RPM), but if your ducting/resonance is tuned so raising redline will make a difference, that engine is going to run quite poorly on the street.)

Gearing can also be a factor. I had a car which struggled at its top speed. Fourth gear was too tall for it to be able to accelerate. Third gear put it past its horsepower peak, so the faster you went, the less horsepower you had. The gearing was all wrong for speed, but it was excellent for street-driving fun, refinement and MPG, which is what I paid for.

A typical non-sporty street car like a Ford Flex is likely to hit physics limits of aerodynamic drag before it hits a point where the computer would rev-limit or MPH-limit.

• It is not "the wind" (first para...) even if the wind speed is zero there will be aerodynamic drag due to the car's speed and air resistance. – Solar Mike Jan 10 '18 at 12:09
• @SolarMike Good point. Edited. – Harper - Reinstate Monica Jan 10 '18 at 16:35
• 25mph on a bike is not easy, it's pretty fast. 40 is nigh impossible unless you're drafting behind professionals and you're a professional yourself, or going downhill. – Nate Jan 10 '18 at 19:15

For modern high performance cars, built after around the year 2000 up until today (2018), the answer is simple: tire grip.

Engine performance and management has already reached a level that can outperform how much grip tires have on the road. What happens when you try to exert more energy than your tires can handle is wheel slip.

Most people would be familiar with wheel slip from standing starts (like in drag racing) and when cars are moving slowly (when people deliberately burn rubber). This type of slip was eliminated by letting a CPU control the brakes (traction control).

Next comes the wheel slip we're concerned with. Wheel slip while moving at top speed. The traditional fix for this was to modify the car's aerodynamics and add down force to basically push the car to the road.

Now we have reached the stage where adding even more down force would increase drag and reduce performance. But our top performing engines can still generate wheel slip.

However, in parallel to engine development, advances in chemistry and tire design have also contributed to increasing a car's top speed by upping the speed the tire is able to handle before losing grip. Now that we have reached a point where our best engines can consistently fail tires the current limiting factor is tire grip.

• I understand that this answer is for high performance cars with very powerful engines only, correct? My question was more general, including also lesser cars, e.g. with top speeds of 100 mph or so. – user1583209 Jan 10 '18 at 12:59
• This needs references. I've never heard of top speeds limited by wheel slip. – Hobbes Jan 10 '18 at 13:24
• I have never heard of wheel slip being a limiting factor with speed. Acceleration, yes. Steering, yes. Speed? – Transistor Sep 23 '19 at 16:20

To find the purely theoretical limit depending totally on limits of the rolling resistance of the tire and air drag. So here is the work.

## Formulas

• $$F_d = \dfrac{1}{2}pA\mu_d v^2$$: this is the formula for drag force.
• $$f_s = \mu_s mg$$: this is the formula for static friction force.

NOTE: I am using values of a Tesla model 3.

## Known values

• A = 0.23 m2
• g = 9.80665 m/s2
• m = 1611 kg
• $$\mu_s$$ = 0.7
• $$\mu_d$$ = 0.23
• p = 1.2754 kg/m3

## Assumptions

• Car is perfectly perpendicular to the force of gravity.
• Car is at sea level.
• Conditions are ideal.
• The power of the engine is infinite.

## Results

$$V_{theo} = 1280.9\text{ mph}$$

You didn't specify a gear-driven (direct-drive) car, for one thing. Even for direct-drive vehicles, the limiting speed is set ultimately by designing aerodynamics to keep the car from taking off and flying.

Last I checked, land-speed records were set with extreme-design cars, jet or rocket-powered, with incredibly specialized wheels and brakes (standard discs would just fly apart at the high RPMs involved) among other parts.

In sum, as new materials are developed with ever-greater strength-to-mass ratios, land speed records are likely to continue to be broken.