Horsepower calculators can help you figure out how much horsepower to reach a certain top speed figure with your car. However, before we get into calculating the amount of horsepower you need to reach a certain top speed goal, let us first look into some of the factors affecting your car or vehicle’s top speed.
In general, top speed is physically a balance point between all of the forces acting on your car. When the total sum of the forces propelling the car forward, are exactly equal to the total sum of the forces holding it back, the car can no longer increase its velocity and reaches a steady state top speed.
In doing so, we have broken down the top speed equation into two primary factors which are:
Force: Represented in horsepower
Resistance: Represented in drag
Breaking it down even further:
The factors affecting how much force your car has behind it are related to:
- The total amount of raw horsepower you have to work with
- The final drive gearing of your vehicle which combines your transmission gear ratio, your differential final drive ratio, and your wheel and tire package diameter
And the factors affecting how much resistance your car has against it are related to:
- The car’s aerodynamic profile which is summed up with a single number called the drag coefficient which summarizes different parameters such as:
- The car’s frontal area (which determines how well the car penetrates through the wall of air ahead of it)
- The car’s height or ground clearance which determines the portions of the airflow that is split and forced both over the roof line of the car as well as under the belly pan of the vehicle
- The car’s side profile which determines how the air is expelled after it passes over, under and around the car and determines the characteristics of the low pressure zone behind the rear window or rear bumper of the car. This zone is always effectively ‘sucking’ the car backwards and needs to be minimized.
- Besides aerodynamic resistance factors, there are also mechanical resistances that come from the high rpm rotation of the engine internals, the transmission, the wheel and tire package, the heavy drive-shaft and axle-shafts (especially on a four wheel drive car for example) and so forth.
Research has shown though (and certain racing classes such as Formula 1 have pragmatically confirmed this) that after the point of about 100 miles per hour that the mechanical resistance factors become less significant in affecting a vehicle’s top speed.
At those speeds, aerodynamic drag is the primary resistive force in deciding a car’s performance which is why in sports like Formula 1, similarly powered vehicles vary significantly in performance based on which car has the proper aerodynamic setting for the best combination of top speed figures as well as aerodynamic assisted traction (down force) during high speed cornering. In comparison, a lower speed racing class such as auto-crossing for example (which is limited by track design to around 80mph for the fastest cars) you find that typically the best performing cars are the ones set up with the best mechanical traction (coming from proper suspension settings and good tire traction) with no real dynamic effects coming from aerodynamic design.
Having said this, gaining an advantage in top speed by altering your car’s drag coefficient can be an expensive process with increasingly diminishing returns. After the first set of basic modifications are exhausted such as…
- Lowering the car’s ride height to reduce turbulence under the vehicle
- Installing an aftermarket front bumper with built in air splitter or extending the factory bumper with an add on air splitter to promote more percentage airflow over the car
- Using lower profile extremities on the car such as lower profile mirrors or rear spoilers with a less aggressive angle (to give a better balance between drag and down force)
- Paneling the underside of the car to give a smooth lower belly-pan that helps accelerate air under the vehicle and reduce turbulence below. (You will find that manufacturers like Mercedes do this on even their lowest level compact cars to improve high speed stability and highway mileage).
- Using a kitted or custom made rear bumper with a built in rear diffuser to improve the transition of the two airflow streams from above and below the car merging behind the rear bumper and preventing that low pressure zone behind the bumper from sucking the car backwards.
- Chopping the top on the car and lowering the roof-line height with respect to the hood and trunk (think of the roof height on a Corvette vs on a Jeep to get a better understanding of why this works)
- Using strategically placed vents in the hood and front and rear fenders to promote airflow through certain high pressure zones (such as under the hood or in the wheel wells) to reduce the pressure in these zones and help increase the airflow through the vehicle
… once this list of modifications is exhausted, you will find that your coefficient of drag may have realistically dropped by 30%. However top speed relates to drag as follows:
Power to overcome air drag = fA x Cd x 0.00256 x mph cubed / 375
Notice in this equation that the cube of the top speed is related to the coefficient of drag Cd and so altering your drag coefficient from a typical 0.45 to a more sporty 0.30 ( a reduction of 30%) only results in a 12% increase in your actual top speed (i.e. going from a top speed of 100 to 112mph)
Yes this is a notable gain, but to do something as significant as doubling your top speed, you’re going to have eventually start to increase your overall power level. This is a realization that was quickly apparent to Volkswagen designers working on the 1100hp Bugatti Veryron and is precisely the reason they had to use so much power to reach their 400 kph top speed target.
So going back to this equation stated above, we know that if a car is power limited in its top speed run (where we have more gears to use for acceleration or where we reach our top speed in top gear much earlier than red line) then we know that increasing the engine’s horsepower to take advantage of the remaining rpm range (or gear ratios) is a very practical way of raising the car’s top speed.
In a practical sense, even if the coefficient of drag is unknown on the car in question, it is possible to calculate how much power is required to reach a certain top speed goal by comparing your current power and top speed levels, with your target top speed level. By doing so, and by using the equation below (derived from the general equation above) we get:
New horsepower = old horsepower * (new top speed / old top speed)^cubed
A practical example that is close to home for me is the 320 horsepower 3000GT VR4. This twin turbocharged car comes with a great aerodynamic shape and is capable in stock form of reaching a top speed of a 160 miles per in 5th gear at 6000 rpms with 1000 rpms to go in that gear and a whole unused 6th gear.
Having the car so obviously power limited (rather than gear limited or drag limited) in its top speed, some of the enthusiasts have gone on to modify this car and break the 200mph barrier.
Applying our formula above:
New horsepower = 320 hp * ( 200mph / 160mph) ^3
New horsepower = 625 horsepower
So what this says, is that to reach a top speed of 200mph in a 3000GT VR4, we know that we will require at least 625 horsepower (assuming that we have enough gears and rpms to increase our wheel rotational speed by 200/160 or 25% while still operating under the car’s redline rpm).
As a final note, it may seem insane to try and double your car’s horsepower and take to a top speed that is well beyond any speed limit you will ever run into on a normal road however:
1- There certain platforms such as the Chevy Corvette, the Mitsubishi 3000GT, the Toyota Supra…etc where doubling or tripling the power levels on these iconic sports cars is not only common practice, but also relatively cheap ($7000 for the 3000GT using Dynamic Racing’s “Diablo Killer” upgrade package)
2- There are also sanctioned racing classes that allow enthusiasts to race their cars on top speed tests as well as standing mile acceleration tests. These are very addictive and difficult racing classes that attract only the most dedicated of enthusiasts to extract every ounce of aerodynamic design, horsepower, traction, gearing, stability and longevity out of their vehicles and have become more of a racing cult or an addiction that is hard to break.