Why Do Horsepower And Torque Cross At 5,252 RPM?

Hello everyone and welcome. If you've ever looked at a dyno plot you may have noticed that torque and horsepower always seem to cross at 5252 RPM torque in pound-feet and imperial horsepower. Now, why does this happen? Well, that's the question we're going to be answering in this video and then the second question does that actually mean anything is there any significance to this number? So we're going to be answering the question using three fundamental basic truth equations, so the first equation power is equal to force x velocity our second equation torque is equal to force x radius so if you think about a wheel you have a force acting on that wheel about a certain radius the torque at that center is going to be equal to force x radius. Now we can of course rearrange this equation and say that the force divide over radius is equal to our torque divided by radius great we've got one equation out of the way next we move on to our third and final equation velocity is equal to distance over time so if you think about a wheel traveling along the ground that wheel is moving at a specific distance per unit of time so distance divided by time and we can also you know state this as the wheel circumference so that's the total distance it will move per revolution so circumference multiplied by the revolutions per minute rpm for instance so the total distance that this will travel per unit of time is equal to the distance of one revolution which is the circumference of this wheel multiplied by the speed at which it's rotating revolutions per minute, okay great so we can now state this as circumference the circumference is equal to π x diameter or 2 x the radius x diameter so we have 2π x radius that's our circumference multiplied by rpm. This is equal to velocity. This is force force is equal to torque divided by radius and we know that power is equal to force times velocity so now we can substitute in each of these equations so we can say that power equals force torque divided by radius torque divided by radius x velocity distance divided by time or 2πr x RPM 2πr x RPM cool well now you can see that you have radius on the bottom as a fraction divided by radius and your also multiplying by radius so we can scratch those out and say that power is equal to torque x 2π x RPM great now a Scottish engineer by the name of James Watt did a little experiment he wanted to know how much work a horse could do in a certain amount of time how much power a horse made so he came up with some equivalent units and in his experimentations and discovery and math he decided that one horse can do 33; so one horsepower could do 33 000 foot-pounds of work per minute. Ok now what's interesting about? This is this is in units of foot-pounds per minute this is in units of pound feet per minute so we can divide the two and that will give us units of horsepower so horsepower is equal to torque times 2π x RPM divided by 33 000. Okay, so if we take 2π over 33,000. We can simplify that fraction to 1 over 5252 so horsepower now equals horsepower equals torque x RPM divided by 5252 so now you can see where this number comes from if you put in an RPM of 5252 you get 5252 over 5252 those cancel out horsepower equals torque, so they are equal to each other at 5252 RPM. Now, does this mean anything the second part of this video? No it means absolutely nothing. It's completely pointless there's nothing exciting about it so if you were to scale these two differently if you were to scale horsepower and torque differently because they're different units they're not the same unit so there's no reason why they have to be on the same scale then this number would change where they intersect would change so if say for example on our scale here this was 300 horsepower but it was 200 torque because each one will have its own axis then they're not going to intersect at that 5252 likewise this only happens if you're using imperial units so this equation with metric units is going to give you kilowatts= Newton meters x RPM divided by 9549 So in metric they're gonna cross at 9549 RPM so what have we learned well we know where the number comes from we know why when you look at a dyno plot with horsepower and torque equally scaled that they will cross at 5252 RPM using imperial units. So it's meaningless but this is where it comes from and if you've ever been curious why, that is the answer. So hopefully you've enjoyed watching if you guys have any questions or comments feel free to leave them below. Thanks for watching.

Channel: Engineering Explained

Views: 1,027,963

Keywords: horsepower, torque, 5252 rpm, 9549 rpm, why, engineering explained, horsepower vs torque, power vs torque, kw vs nm, audi, honda, bmw, mercedes, dodge, jeep, chevy, ford, subaru, mazda, nissan, toyota, vw, acura, lexus, infiniti, hyundai, kia, ferrari, Ram, Cadillac, GMC, porsche, fiat, jaguar, lamborghini, maserati, aston martin, alfa romeo, mclaren, koenigsegg

Id: lt7iUBE3_AE

Length: 6min 7sec (367 seconds)

Published: Sun Jan 21 2018