Why Do Hp and Torque Intersect at 5,252 Rpm?

Posted July 09, 2019

By Dean Larson

Photos: VL Performance

Videos and mathematical methodology by Jason Fenske of Engineering Explained

Is that a pointless question? Well, I guess it depends on who’s asking, but inquisitive minds may inquire when you find out that the horsepower and torque curves of a gasoline engine will always cross at 5,252 rpm.

I first heard this factoid at a grassroots hot rodding event recently, where there was a dyno trailer and a line of good ol’ boys waiting to test out their machines. I was watching the action and talking shop with a man in a fedora who pointed out the 5,200 (or so) rpm anomaly, but said he really didn’t know why that was the case.

I blurted out the only spitball answer I could come up with, which was that hp and torque were related to one another, so the 5,252 must come from some constant or something. Close, but not quite.

Back at the office, I remembered the conversation with the graybeard at the car show, and entered a crude version of my question into the all-knowing Google search bar. The answer to my question, and indeed much more, came from an intelligent young man (with some grays himself) named Jason Fenske who operates a YouTube channel titled Engineering Explained.

A mechanical engineer with a passion for cars, Fenske explains the mathematics behind engines, transmissions and driving characteristics, in a matter-of-fact manner that most of us can understand (well, after watching more than once anyhow). Fenske’s videos have been viewed 356,467,822 times — so you’re welcome for your next work distraction.

The explanation offered by Fenske focuses solely on the manipulation of known equations to eventually relate power, horsepower and torque. By substituting and canceling out terms, Fenske eventually arrives at an equation with just three terms: power, torque and you guessed it — 5,252.

If you liked the video but think you missed a few things, I encourage you to also watch the Engineering Explained video on horsepower versus torque. It helps set the stage for some of these terms, and is a much better explanation than the analogies you’re used to like: “horsepower is how fast you hit the wall, torque is how far you take the wall with you.”

Equations 2


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