# Why does a gas engines torque and horsepower curve always meet at 5252 RPM?

I'm watching a TV show called Tech Garage and they just made the claim that an engines torque and horsepower curves always meet at 5252 RPM. Assuming this is true, why does this happen? Is it something designed into engines, or is it just how the thermodynamics work out?

If it is a result of design, what about the engine is arranged to make it true?

• From what I understand all engines have that same intersection. Weird. Jan 22 '16 at 4:35
• I wanted to ask this question for ages.. +1 Jan 22 '16 at 10:58
• This misconception seems to come from the oft repeated notion that horsepower and torque are vastly different things, when really they are based on the same measurement, distinguished only by whether it additionally factors in engine RPM (in the case of horsepower) or does not (torque). Glad this didn't turn into a "torque vs horsepower" thread! Jan 22 '16 at 19:09
• Sounds like that would be as bad as a "PC vs Mac", "Canon vs Nikon", or "Chevy vs Ford" thread... lol Jan 22 '16 at 20:38
• So basically "Since V=IR, why are V and R the same number when I=1?", but for rotational mechanics rather than electricity, and in silly units where the reason isn't obvious. Jan 23 '16 at 6:10

## 3 Answers

It's just math, and is because horsepower is defined (in terms of torque) as 550 ft·lbs per second.

A single HP is 33,000 pounds moved 1 foot in 1 minute (as per James Watt, that's the average of what an actual horse can do). An RPM of an engine moving the same 1 lb would travel ~6.283ft (the circumference of a 1 foot radius circle).

33,000 / 6.283 = 5252

• Comments are not for extended discussion; this conversation has been moved to chat. Jan 22 '16 at 20:28
• "An RPM of an engine moving the same 1 lb" - shouldn't that be "the same 33,000 lbs"? Just making sure. Jan 22 '16 at 21:33
• @jedd.ahyoung It's moving 1lb over 33,000 ft vs 33,000 lb over 1ft. Same amount of work and power. Jan 22 '16 at 21:40
• Where did the 1ft output radius come from? Jan 22 '16 at 21:42
• Yes. I think the phrasing in this answer could be improved, thoufh Jan 22 '16 at 22:13

Just for fun, I did some math in google, to show that this is an artifact of the unit system being used to put numbers to torque and power.

The number 5252 can be calculated as:

``````1 horsepower / 1 lbf foot radian in turns/minute
5 252.11312
``````

The exact number is 16,500/π (33,000/τ)

So, if the math were done in metric units instead (watts, and and newton-meters for torque), you would get:

``````1 W / 1 N m rad in turns/minute
9.54929659
``````

This number happens to be 30/π (or 60/τ), due to the number of seconds in a minute. If you measured engine rotation speed in radians/second, the number would become 1. The same would apply to the non-metric system, if foot-pounds were used instead of horsepower to measure engine power.

Where the "curves meet" is entirely an artifact of placing both quantities (measured in horsepower and pound-feet) on the numerically same scales on the axis of a graph. If you graphed them against each other rather than against RPM, this would instead show up in that some point (corresponding to 5252 RPM) would show up at a point where the power in horsepower and the torque in pound-feet are the same.

• Beauty. +1 out of votes today. After UTC I will. TY for quality info. Jan 22 '16 at 21:36
• so, it's an aertifact, they don't actually meet because they are measuring in different units. Jan 24 '16 at 4:54
• +1 for calculations. Considered rescinding +1 for use of tau. Just kidding :) The Tau Manifesto and The Pi Manifesto, for those who are confused. Jan 26 '16 at 21:42

Just adding to Marks great answer above:

Although horsepower is defined in terms of torque, horsepower is the more useful measure of an engines output when it comes to trying to figure out how fast your car will be, assuming you have an appropriate transmission. A transmission alters the torque output, but leaves the horsepower unchanged (neglecting friction losses, etc.). Therefore, the old saying "horsepower sells cars, torque wins races" is actually completely false in theory. A hypothetical engine that made 1000ft-lbs of torque, but only revved to 10 RPM would result in a painfully slow car.

For actual cars, though, people rarely ever discuss the actual horsepower or torque curves. They usually only talk about peak horsepower or peak torque. Cars with high torque usually produce it in the lower end, and this also raises the horsepower in the lower end. Because horsepower is related to RPM, peak horsepower typically comes at high RPMs. Therefore, a 'high torque' engine may have the same peak HP as a 'low torque' engine, but the high torque engine will have more horsepower in the lower end of the RPM range. Because of this, the car will be faster - but people who only consider peak values will say that this is due to the torque, when really it is due to a broad horsepower band. Remember - any engine can in theory produce an arbitrarily large amount of torque after being routed through a transmission.

For a simple hypothetical example, consider an engine A with a typical horsepower curve, then imagine an engine B with the same exact horsepower curve, but scaled x2 on the RPM axis. If engine A produced peak HP at 5,000 RPM, engine B would produce peak HP at 10,000 RPM. If engine A produced 90 HP at 2,000 RPM, engine B would produce 90 HP at 4,000 RPM.

Now, imagine routing engine B through a frictionless transmission with a 2:1 ratio. This will effectively slow down engine B, so that the features of the transmission-modified horsepower curve now occur at the same rotational speeds as engine A. Engine B is now producing the same exact torque and horsepower output as engine A after the transmission, despite the fact that engine B would clearly have less torque before the transmission. (Again, see Marks great explanation of the math)

• Yes, but you totally ignored torque there. Remember what "actually moves the car"? Assuming both engines had the same torque, ( you never specified ), then engine b would definitely outshine engine a because with a 2:1 gear reduction, engine b, without friction and heat accounted for, would have doubled its torque factor most definitely sealing a victory over engine a. In the simplest of terms- torque is the basic strength of an engine, being weight moved a specific distance (work), while horsepower is merely the RATE at which an engine accomplishes that work, being expressed as weight moved a Feb 11 '18 at 8:04
• But I did specify torque at a few rpms... implicitly. Engine A produces 90 hp at 2000 rpm, so it has 263.3 ft-lbs of torque (at that particular RPM). Engine B produces 90 hp at 4000 rpm, so it has 118.2 ft-lbs of torque. At the output shaft of the frictionless transmission, engine B still produces 90 hp, but the output is now slowed to 2000 rpm, so it has 263.3 ft-lbs of torque. Jun 7 '19 at 23:08