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.