Does an increase in horsepower allow a greater speed in any given gear?

I wasn't sure if this was the best place to post this, or if I should go post it in the physics stackexchange as well. I can crosspost if this question would be more fitting over there.

To put this question in context, take my car for example. Before winter, I had installed an aftermarket air intake, which claims to increase the power output by about 4 or 5 horsepower. I noticed that when I redlined in 3rd gear and shifted into 4th, I was consistently at 93 or 94 mph. I recently swapped the intake back to the stock intake, and since then, I have been consistently leaving 3rd gear at 90 or 91 mph - and that's redlining through all gears.

A few of my friends attribute this to user error, in that I am evidently not shifting as efficiently as I was whenever I had the aftermarket intake. Some of my other friends argue that these 2 or 3 extra mph in 3rd gear could have come from the extra 4 or 5 horsepower that the intake gave me. Is this feasible?

I am essentially just wondering if it is possible for an increase in power output to result in a higher speed being reached in each gear, even if I am on the same gear ratio. Is the speed reachable in each gear directly proportionate to the gear ratios, or can this speed be influenced by the amount of power being put out by the engine? Thanks in advance!

• No, but the extra power will change the rate of acceleration... Commented Mar 6, 2018 at 18:04
• Have you ruled out the effect of tire tread, tire pressure, road surface/condition, weather, etc? All of these could be the cause of the difference Commented Mar 6, 2018 at 20:56
• Tire pressure will definitely change what mph you reach redline. Outside air temperature is enough to cause this, as well as how much energy you put into the drive tires (by repeated acceleration runs, turning hard, braking hard, etc.). Tires are flattened where they are in contact with the ground, and that's what determines the actual radius of the wheel when the car is being driven. Commented Mar 7, 2018 at 3:24
• If you are power limited instead of rev limited, the power demand rises with the cube of the speed. Conversely, the speed goes up as the cube root of the available power. You don't say what power you had before, but an additional 4-5 will not add much speed even if you are power limited. Commented Mar 7, 2018 at 16:15

No, HP does not determine MPH in a gear, the gear ratio does. Although there are hypothetical ways that HP can seem to make the vehicle go faster in the same gear, it doesn't actually change the speed capacity of that gear as long as the engine RPM is limited.

As noted, the answer is no... or at least not really.

In lower gears, the gear becomes the limiting factor because there's only so many RPM that the engine can perform. In higher gears, the engine does become the limiting factor because the gears allow sufficient feedback and resistance to the engine that it can't keep pushing.

As an example: Say your in a gear with a 2:1 ratio and you're traveling 60 MPH. At this point, we can say you're getting 'x' amount of resistance from wind, but with the 2:1 ratio, only 1/2'x' is making it to the engine in the form of resistance. If you shifted gears into a 1:1 gear, then the engine would be fighting a full 'x' of resistance.

This is why if you have a very open, high-speed gear (like most cars' final drive gear) your engine doesn't (typically) produce enough power to totally overcome the various resistances that are in play. The clearest example of this is when you're driving up a steep hill in 3rd and you notice how much sluggishness there is. When you down-shift, suddenly you can accelerate much better. This is because in the lower gear more power is being used as torque and therefore less resistance is transmitted to the motor and your engine can now overcome that resistance. You engine didn't get stronger by down-shifting, but the way that the power is being applied did change.

If you're more interested in understanding a lot of the physics that are involved in translating a car's power to its speed, check out this "Advanced" article. I do stress that it's actually "advanced" meaning that if you're not up on physics and the maths, this may be pretty confusing. But if you avoid the equations, there's plenty of text that helps increase the understanding here.

Raising the engine's HP output will (generally) raise the HP curve along the entire second half of the chart. So this does mean that at redline (say 7500 RPM) you’ll have a little more power than previously. This can mean getting a little more “oomph” to the wheels between bounces off the rev limiter, but that will (if at all) barely affect top speed.

When your gear ratio is say 2.5:1, then it stays 2.5:1 regardless of total power output. Your engine is rotating 2.5 times for each wheel rotation though the amount of persistent force is greater. This is why these monster drag cars often have 1 or 2 forward gears. The sheer amount of power lets them blast into motion and keeps persisting against a really wide gear ratio. So:

Is the speed reachable in each gear directly proportionate to the gear ratios

Yes

And:

or can this speed be influenced by the amount of power being put out by the engine

Yes. But not directly. Since we're talking about a mechanical system there are variables in the system itself that will affect overall speed. So the speed can be influenced, but only indirectly.

As Solar Mike said in the comments, though, the added power will reduce the time it takes to reach a given RPM. What could be causing the difference is that the added power is pushing you deeper into the red zone - faster - thus achieving a slightly higher actual RPM before shifting. And depending on the gear ratio, even a change of a couple of RPM could create a 3-4 MPH difference.

I'll also add that it varies this entire argument if you're shifting when the tachometer reads redline, or when you actually hit the rev limiter.

• I'm reluctant to downvote because the facts are correct, but this answer seems so full of minutia that doesn't apply at all to the modest gains you MIGHT get from an air filter and therefore clouds the answer which is very straightforward for a very straightforward reason. I like that you give lots of info, but personally I would have worded it, "no, absolutely not in your case, but in theory more power might make a minuscule difference in these cases..." Commented Mar 7, 2018 at 18:56
• @seizethecarp I edited a bit and added a bit. I appreciate the criticism cause I do want to get the info across and keep it from being too confusing or hard to read. :) Commented Mar 7, 2018 at 20:53
• That's a great addition! And thanks for taking the critique well; you're a better man than I usually am :P Commented Mar 8, 2018 at 17:29

The answer is no because you mention being limited by your redline. Regardless of power, a certain RPM will result in a certain speed for a given gearing. Chances are the gear ratios were chosen based on the factory output of the engine.

However, for other cars this may not be the case. Because of wind resistance (in many cases) a vehicle may not have the raw power needed to reach redline in their top gear. In this case, more power can translate to higher speed since it was not mechanically limited.

• That’s kind what I’m saying... it’s most noticeable in final gear, but in all gears the power does affect the ability to reach, and time it takes to reach a given RPM. With all the variables of the system, then power can create the appearance of greater speed potential. Commented Mar 6, 2018 at 18:49
• @kyle_engineer, if your car can reach the redline then yes, the best more power can do is make the car "feel" faster, because you can get up to speed quicker. Your 1/4 mile time would actually be faster, but your final top speed wouldn't change. Commented Mar 6, 2018 at 18:51
• exactly! But is it possible that depending on rev limiter design that some added power will achieve a higher RPM even if it’s not momentary? I’d think “yes” but honestly I don’t know the various methods of rev limitation all that well. If the engine had no limiter, then it would achieve a static RPM when you top out a gear, but if there is limiter bounce then I could see that creating a small affect... no? Commented Mar 6, 2018 at 18:55
• @kyle_engineer If there is no rev limiter, and the engine has enough power, it will destroy itself by spinning too fast. If there is a limiter, it does depend on how it works, but a stronger engine could recover from the "bounce" quicker and maybe give you a higher average top speed, but the instantaneous top speed will be reached when the limiter kicks in no matter what. Rev limiters operate at very high speed and will cut spark or fuel or both almost instantly so I don't think you're going to jump over the limit even with more power. Commented Mar 6, 2018 at 19:03
• ok, that’s basically what I’m thinking. But since speedos (especially cheaply made digital ones) have a delay, then the “higher average speed” could appear to be higher. Because this delay wouldn’t drop as much if the bounces are shorter... that’s my logic anyway. Not sure if that would actually pan out that way ever, but it seem like it could hypothetically. Ergo my conclusion that “depending on the variables of the system” it could appear to increase overall speed. Commented Mar 6, 2018 at 19:07

Well the simple answer is (as you suspect)... No.

With fixed gearing, you are going to be doing the exact same speed at any given engine RPM with 100bhp or 600bhp.

Let's forget the power for a while. The body of your question shows that you're in fact interested in this: can a custom air intake influence the exact RPMs at which you "redline"? Well... yes, sort of.

That depends on rev limiter. Some are of "soft-cut" type, which means they have an RPM range where they act, not a single red line. In the operating range they throttle (or retard) quite rapidly, but proportionally to RPM. The actual red line is simply the point when the engine power output is in equilibrium with the power input required by the vehicle.

In other words, with soft-cut rev limiter that point of equilibrium slightly depends on how much engine power output responds to a constant throttle.

So yes, the custom air intake increases power and somewhat shifts that equilibrium. If it happens at 2% higher RPM, you have exactly 2% higher speed with the given gear (for example 93 mph instead of 91 mph).

To add to other answers, the only time extra horsepower will increase speed in a given gear is for top gear, as often the maximum speed is where the engine runs out of power to overcome rolling/air resistance and the car does not reach the redline in top gear no matter how hard you push. Extra power will allow more of the rev range to be usable.

Example - the Toyota Supra mk4 is geared sufficiently (transmission, final drive and tyre sizes) to reach 200MPH at the redline in top gear. However, even this powerhouse of a vehicle doesn't have the necessary oomph from the factory to reach it - 320HP isn't enough. Around 180-190MPH, it'll stall out. So it won't reach the redline without more power.

Other than that, the wheels and engine are mechanically linked once the transmission is fully engaged, and thus one RPM of the engine directly translates into the mathematical product of the transmission at the wheels - this cannot be changed. Clutch slip or the automatic torque converter can allow the engine to run faster than the transmission, but that's the opposite to what you describe.

I would also like to point out, as a petrolhead, that constantly redlining your car in everyday use is really, really hard on the engine and quite unnecessary. It also really kills your gas mileage! Usually you can upshift at around 3-4,000 RPM without losing the power curve on the next gear.