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

Hope everyone's having a wonderful day! If you're watching and confused about what the difference are between Horsepower and Torque, I have a previous video to sort that out: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-u-MH4sf5xkY.html. If you're watching this video and you're thinking, what the heck, math!? We all feel similarly haha. If you're watching this video and thinking, really I just want to see pictures of cars and the sort, here's my Instagram: instagram.com/engineeringexplained/

Put a mic on that marker so we really hear that squeak good

And if the lines actually cross at 9549 rpm you not only have a metric chart, but more importantly an amazing engine.

As a Mechanical Engineer myself, believe me it took awhile to understand the concepts during the process of obtaining that degree. Curiousity with how things worked along with being a gearhead kept me in play. Its a matter of sticking with it and lots of study. Love the Channel !

"it's completely pointless"...died laughing there and continued to watch :P

Pointless you say yet I feel smarter after this video...I'd definitely give this channel most informative award.

So glad you actually put science behind it. So many do not understand tq, hp, and how a dyno works.

Unit cancellation is so satisfying...

This video is exactly why I love this channel, it's entertaining and informative and Jason is honest about how this doesn't really mean anything :)

Clips like this is why I watch. Im off to spread useless but interesting knowledge

If it wasn't for you I wouldn't know half as much about cars as I do.👍🏻👍🏻 keep it up

Great explanation. Please do a video on "why most cars develop maximum torque at mid-range RPM instead of at high-range RPM" and "why the best acceleration effort of the engine occurs when the engine is churning-out approximately half of its total power rather than when it's churning-out all of its power." Once again, thanks for all your great videos. Please notify me when you do the video in suggesting.

I've never enjoyed a meaningless piece of information so much.

You explain things with engineering basics that's the unique thing about ur channel. Satisfys that inner nerdy engineer in me who wants to know why and how based on facts. Grt job

Always a well-made video. Good to see the whiteboard back in action!

Jason is really a wizard, he just chooses to shave his silver beard to go incognito.

Funny coincidence, we had been doing an assignment/having a discussion in class about horsepower vs. torque when your last video was published a few days ago. There were a few questions from my students about why you never mentioned the 5252 thing. Well, here ya go!

Never knew this! Now I will have something to talk about at the dyno tomorrow instead of worrying if my BRZ will break 150ft.lbs of torque 😐

My car's redline is 4800 rpm😹

I love when formulas are explained in a way that I can grasp. Well done. I learned something and I enjoyed it.

Best way to spend 6 minutes learning something absolutely pointless xD

God I love this channel.

This was definitely a mathematic nerd out in which I enjoyed. :)

Interesting to note, if you use the proper Si unit of angular velocity (rad/s), kW and N*m should cross at exactly 1000 rad/s.

engineering explained your all in one channel for car guys and everyone wants to be involve in automitive tech or industry

I feel smart!!! I already knew the exacts reasons and maths behind this from engineering school. Always had an interest in both cars and engineering, and it was annoying in my youth not being able to explain to friends that hp and torque are related, and not independent.

Funny, I was looking for this formula yesterday whilst working on my dissertation project. Decided to watch this on my lunch break today and voila!

Imperial user here , still watches. Nice video ! But in metric 1HP=749W, So how can it become 9549?

are all these videos one-takes? maybe I'm not watching close enough but that would be bloody impressive, especially with all the info that needs to be A, remmembered, and B, spoken about in a clear and coherent way, possible that there's a script or some sort being shown off-camera but even so, well done Jason!

Nice. Just a little tidbit I never thought about before. Cool video.

I've watched a lot of engineering and technology fellows try and explain stuff. They tend to enjoy doing stuff like paid promotions and a lot of weird drama can tend to get involved. I've always enjoyed your channel because your one of the few channels that sits here and goes. LOOK! THIS IS AN OPINION! ok, now that that is out of the way, here are all the base facts, regardless of my opinion, and how they stand. When your opinion is interjected, you will straight up say, I know my opinion is silly, so here are the facts, I still have my opinion, but I'll let you make your own opinion. You ALWAYS give the facts and even correct yourself when you make mistakes (which is FAR fewer then most channels) and you do an excellent job with how you present yourself. I love it because I know I can get EVERYTHING unbiased from you and it's all just number crunching and realistic stuff with you. Thank you for being awesome and keep doing what you're doing!

should have did a mic drop with the marker and walked off frame, nerd cred

Thank you for this video I grew up building engines my father was a racer and I learned that a properly designed engine would do as you say but I never understood why till now. No one taught us anything except the bare minimum back then.

You inspired me to become a mech-e!

You are the Brian Cox of car stuff, and its AWESOME!!!

Nothing quite like a 6 minute video that ends with "in the end, it's pretty much meaningless but thanks for watching"! Honestly though, it was an interesting video even if the magic number is meaningless.

You brought back some fond memories. In the late 80's I was a Dyno Tech in the engine overhauls shop at a Detriot Diesel dealership. My job was to take every engine that had a fresh out of frame major overhaul, do a break in run, then full load dyno tune (someone else ran the in frame overhauls on the chassis dyno). I vaguely recall using the Torque X RPM ÷ 5252 equation to figure HP because our dyno only displayed torque. Thanks for this, and all your other videos. Subscribed!

Best 6 meaningless minutes I spend today. Good work!

“It’s pointless, completely meaningless, and uninteresting” he says as I’ve been completely glued to the video in pure interest and understanding😂

I'm pretty sure the intersection at 5252 (in imperial units) does allow me to make one assumption... When a vehicle's peak power rating is higher than it's peak torque rating, I know it's a relatively high performance engine (or at least that it's power peaks above 5252rpm).

Saw this Video Title a week ago but never watched... Then I started noticing all Dyno Charts meeting at 5252 and it started to drive me crazy!!! So, here I am watching why! Thanks!!

That's when the VTEC kicks in!

Jason, you excel at what you do!

Engineers. Putting two different units on the same axis.

Jason, you have the power to make me feel smart because i understood your clear explanation.

At first I was like, "oh God algebra." And then at the end I was like, "oh that makes sense."

Great video, in fact I was curious about this exact thing but now I know. This saved me the google search for that hp to ftlb/min conversion. Much appreciated.

Math is your thing, that's the thing that sets you apart from other channels. keep 'em going, It doesn't matter if it's pointless math, or if I get lost halfway of the video, I'll catch up with you eventually.

It can't be meaningless: you made a video explaining the math and i watched it!

Would it be any more efficient to have smaller pistons working together or fewer larger pistons?

Pedantic Point: Imperial Units were adopted in the UK in 1825-26. In the US, we use "The United States Customary Units System" formally adopted in 1832 which was mostly developed from the English System (actually the Winchester Standards in use till 1825) There are many significant differences between the Imperial and USC Systems. For example, it takes 1.2 USC Gallons to equal 1 Imperial Gallon. Now the UK and most everyone else use the Units SI (Metric System) while in the US we use both the USC and the Metric System depending on the industry or product.

My brain hurts now

this channel just keeps getting better

But european often use other Units than kW like bhp in england or PS in germany

That was a great explanation, Jason. Whenever I'm asked, I usually just tell people that, basically, one is a force, and the other is a rate. Also, to answer one of your commenters, when you're talking about torque, it is lb-ft, and when you're referring to the unit of work, it is ft-lbs. The automotive engineering industry reversed it in order to distinguish what was being discussed... Thanks for another great video, Jason!

Praise Be

The 5252 rpm figure can be calculated by using a shaft that is 1 foot in circumference and turn it 1 revolution. This means that the diameter of the shaft will be (using inches now) 12 divided by 3.1416= 3.819 inches. The radius of the shaft is 3.819 divided by 2=1.909. then if you apply a force of 33,000 lbs against it you will get a force of 33,000x1.909=63052.2 in lbs of torque on the shaft. Put a lever 1 foot long on the shaft and divide 63052.2 by 12 and you get 5252.1 lbs at the end of the lever. To get 1 horsepower turn the shaft at 1 rpm. So 1 horsepower = 5252 ft lbs at 1 rpm.

Thanks so much for all your videos , you are a great ING.

Because horses

Insightful, interesting, and informative as ever - thank you for the video!

Wait, what?

This has to be the first video of yours that went straight over my head.

is this guy 25 or 45?

In a rotatory system Power is RPM times Torque adjusted by a constant that depends in the system of units used, that is: Power = C x RPM x Torque, where C is a constant. If HP is used for Power and lb-ft for Torque C = 1/5252. From the equation is easy to see that at 5252 RPMs Power(HP) = Torque (lb-ft).

My redline is 5400 so does it still cross at 5252?

you the best engineering explaining yt channel

it's not different for every engine ??

So basically, they cross at 5252rpm solely because the definition of "horsepower" is based on some guy's arbitrary decision to settle on 33,000 for the amount of work his horse could do in a minute - the calculation of which was based on his arbitrary definition of "work". How did Europe define the kW to wind up at 9549rpm?

Excellent explanation, very good to know!

3rd view before the hundreds of thousands!!!

I think the part where you said that the scale of the graph changes the visual representation of where horsepower and torque intersect on the graph without mentioning that regardless of that situation as soon as your RPM is 5252, the number representing horsepower and the number representing torque will be identical. I think that part might confuse some people.

And we learned nothing today :D

Thank you for explaining that this happens when they are using the same scale on the left. I looked at my dyno chart and they were crossing at the same point (both before and after a tune), but they were crossing around the 4800rpm mark. But torque was on the left and power was on the right. Different scales. Great video, thanks a lot.

A meaningless video. Thanks, Jason! LOL

interesting, as always! And thank you for thinking ot the outside world and including metric units :)

Indeed, its no more significant than the fact that distance travelled in miles is the same as journey time in minutes at 60mph. True by definition.

Jason, you salt & peppered genius. Thank you for answering my question.

Two eyeballs staring back at you...with one eyebrow raised. Well that changed my thinking.. I was under the impression that the intersection of HP and Torque was the sweet spot for efficiency and power? Now you tell me it's nothing - nada - nope! I'm left feeling empty... In fact it seems intuitively deceptive to represent Torque and HP on a graph like this because our attention is drawn to the intersection point - but it represents nothing?

Up until now, I never did know how horsepower was calculated; but, I was curious. Thank you.

Thank you for the excellent explanation

In metric that would be P=F*v=F*2*pi*r/t=T*2*pi*f -> P/T=2*pi*f. So, the ratio is proportional to frequency and P [W] and T [N*m] are equal in numerical values at 1/(2*pi) [Hz].

VERY well explained and presented! Opened my eyes to a couple things....Thanks!

That is really well done and a most apropos subject to demystify dynamometer tuning. I never gave a thought to Imperial units vs. ISO metric units determining the "cross over" figure. One thing I would like to have seen is the expression of R.P.M. as "R/M" - Revolutions over Minute. That would make the cancellation of the minutes unit more clear. Compare how R.P.M. is expressed to the horsepower equation: 33,000 ft.-lbs./min. The "minute" unit is in the denominator.

Your teachings could have caught my attention in high school and I probably would have finished instead of dropping out getting a job and my GED a year before I was supposed to graduate

I can remember working of the instrumentation of some very old engine dynamometer - pre digital instrumentation. The RPM measurement was made using a permanent magnet generator hence the output voltage increased as a function of RPM which was indicated on a large analog volt meter that was calibrated in units of RPM. The torque was measured with a torque reaction spring and the amount of reaction was measured using a variable resistance unit that was configured as a variable voltage divider. The input to this variable resistance divider was fed a DC voltage and the output of this variable resistance divider was a voltage that was also used to drive a large analog voltmeter. This second analog voltmeter had a dual scale - both torque in foot-pounds and horse power. Below this meter was a two position switch that allowed the meter to be switched between reading out torque or horsepower. This switch was set up to determine what the voltage source was that fed the input of the variable resistance divider that measure the torque reaction. If the switch was placed in the horsepower position then it would feed the voltage generated from the RPM sensor (generator) which would result in the variable resistance divider performing the multiplication function to calculate the horsepower. If the switch was placed in the torque position then it fed a constant DC voltage to the input of the variable resistance divider. I was charged with the task of calibrating this instrumentation which resulted in the need to calibrate the various parts in a very specific sequence - the RPM meter was first calibrated by adjusting a scaling potentiometer for the RPM meter. Once the RPM meter was scaled the next stage was to calibrate the DC voltage for feeding the variable resistance divider for the torque measurement. This involved spinning the dynamometer to 5,252 RPM and measuring the output voltage from the RPM generator. This measured voltage was the voltage that the fixed DC power supply had to be adjusted to that fed the input to the variable resistance divider. The next step was to adjust a potentiometer for getting the torque meter to read correctly with this DC voltage applied and a fixed known weight on the torque reaction arm to simulate the effect of an applied torque. Once this was completed the entire instrumentation was calibrated - there was no actual calibration step for calibrating the horsepower reading as it had to be correct based on the underlying mathematics.

I always thought it was a fallacy when people say the crossover on the graph is your ideal shift point. To me it just seemed like a product of scales and units of measurement that mean nothing in particular. Now i know for sure lol

"and it's completely pointless" sounds so much better than "because I said so" ( 9th grade math teacher's fav) --Like your style man!

Best video yet! You should make more physics based car videoes.

As always Jason, expertly demonstrated and explained. Sadly most car enthusiasts won't understand any of this, but what can you do...

So glad you finally explained this.

Back in a time before calculators I spent an afternoon at a car museum with an engineer who would do those calculations with a slide rule. It was all magic to me at the time and it wasn't until a couple of years later when I got to college that I figured out how he did it. Great explanation.

so simple and beautiful thanks

thanks a lot for all the great videos that you upload ! it is of great help .. keep the good working throttling 😇

Before watching the video, I'm going to hypothesize that it is a mathematical thing based on how torque and horsepower are calculated and it really means absolutely nothing because the two lines are two different things with two different units. Bazinga!

Best educational video i've ever seen :D Your channel is a goldmine of informations, thanks for everything !!! (I'm working at the French Motorsport Federation, and I sometimes watch your videos to give some technical advices ;) ) Keep up the good work \o/ Cheers, Donnie

Feels like going back to maths class that i hate alot but when Jason is the teacher there's nothing to complain about!

for those who wonder, when u use HP/Nm they will cross at 7121 RPM

Now looking at a dyno sheet I can forever spot the correct units by looking at the shape of the curves. Thanks. :D

I appreciate your simple explanations of the math involved n engine design. Being the nerd that I am I use these constants often. I am amazed that very few people understand BMEP.

All works well as long as time is a constant which modern understanding means, It is not a constant. Not only is it relative but compresses and expands at various points along its progression.