# 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, 2016 at 4:35
• I wanted to ask this question for ages.. +1 Jan 22, 2016 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, 2016 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, 2016 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, 2016 at 6:10

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, 2016 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.
– user11129
Jan 22, 2016 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, 2016 at 21:40
• Where did the 1ft output radius come from? Jan 22, 2016 at 21:42
• Yes. I think the phrasing in this answer could be improved, thoufh
– user11129
Jan 22, 2016 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, 2016 at 21:36
• so, it's an aertifact, they don't actually meet because they are measuring in different units. Jan 24, 2016 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, 2016 at 21:42