Dot Physics gets Power wrong

Rhett Allain has a great blog at Wired.com, but I will not create yet another account just to comment there so my comments will be here instead.

Usually he is on the money, but in this case his bad experiences with ESPN Sport "Science" gets in the way of his analysis of a video about the power of NASCAR cars. For convenience or future reference, I'll embed the video here



and then get to the analysis.

Rhett first objects to the statement that the weightlifter being shown "exerts about 1 hp per rep". Yes, they meant "during", but what is wrong with that? The numbers are right if you take the 275 pound lift as being 2 feet (61 cm) rather than 50 cm (about 20 inches) in 1 second. The weightlifter is producing pulsed power during the lift, which is about half of that 1 second rep, but hardly resting during the other half.

Check out this video of a power lifter doing 26 reps on the NFL 225 pound lift, or this one where the guy does 72 reps at 225 pounds. The first one takes around one second per repetition, locking the arms out each time. The second one is a much shorter, but faster, lift that might make for an interesting video analysis to see what his power output is.

Estimating the average power is trickier, because you really can't use the work done ON the weights as your metric. If you did, the average power would be zero because there is negative work done on the weights as you lower them! !! However, if you shift your focus to the work done by (within) the muscle, it might be more than 1 hp for the entire time the weight is moving. Controlling a weight as it comes down is not quite as hard as lifting it, but it isn't being done for free!

What I like best about this example is that "power lifting" is one of the few cases where a physics term is used correctly in sports. Power lifting, where the emphasis is on multiple reps, is entirely about the rate of doing work in a way that reflects what is done in competitive athletics rather than just lifting the most weight. That is why the NFL tests on the number of reps of 225 pounds. (The NFL record is supposedly 43.) Yes, that is power. And I think it is more obviously power than the similar output required to climb a mountain on a bicycle even though that is probably the most extreme case of continuous power output by humans.

Rhett next complains about a statement that he actually misinterprets. The statement in the video (around 0:50) is that horsepower of a car engine is "calculated by measuring torque". This is 100% correct. Rhett says "First, horsepower is not measured by calculating torque (at least not in physics)." Right but not relevant, because they don't calculate torque. They measure torque and rpm and calculate power by multiplying the two together. Rhett says "I guess the only problem here is using “fast” to describe the relationship between torque and power." except that is not what they are doing. They are using fast to describe the angular velocity, just as you might use "fast" to describe the linear velocity if you said that power was about how fast you can apply a force (Power = force * velocity). This is 100% good physics. Rhett, you messed up this time.

For the record, in physics and engineering and the real world of dynamometers, you determine horsepower by measuring a torque curve (torque in foot-pounds as a function of angular velocity in rpm) with a load cell (which measures force) on the end of a lever that is connected to the load on the engine. Modern ones do the multiplication and plot both power and torque versus rpm, but the actual measurement is torque (or, if you like nits, force that gets autoscaled into torque on the graphical output).

I'll go along with the final nitpick about lifting the space shuttle. Yes, they should have included "in one second" at the end of that last sentence. 850 hp is, indeed, like bench pressing the space shuttle in one second. Time is important. But no one would confuse using a jack (in his video example) with "benching". Everyone knows that you bench press a weight in less than a second unless you are totally whipped, so the same would apply to benching the space shuttle.

My negative nit pick: The video correctly describes the historical origin of horsepower as a marketing term, but the draft horses shown in the video (e.g. at about 0:30) produce more than 1 hp. James Watt used the small horses used in mines as his reference point for selling his steam engines.

My other negative nit pick is that engine size is not nearly as important as the rate of fuel consumption. After all, a top fuel dragster only needs about 550 cu.in. (compared to 358 cu.in in NASCAR) to make over 8000 hp (rather than 850 hp). It is all about the fuel and the rate you can burn it -- and how long the engine lasts! You have to put power in to get power out. Like the co-host commented during his 259 mph test drive of the Bugatti Veyron Super Sport on "Top Gear", before the pro took it to 267, you can actually see the gas gauge moving when you are burning 1.7 gallons per minute pushing out about 1200 hp. Wide Open Throttle is like that. (I'll have to save for another day the effort to figure out the Reynolds number comparison between air and treacle they used. I like it, but I'm not buying it.)

But I also have a positive nit pick. I loved their description of the added power from opening up the exhaust, although they oversimplified it a lot. Part of it is to "tune" the exhaust so it resonates at a frequency that matches the rate at which you want to pull exhaust out of the cylinder. Back pressure from the exhaust makes the engine less efficient. Getting a rarefaction as the exhaust valve opens is ideal.

However, the distinctive engine sound they played comes more from the Doppler effect than the resonating pipes. You need to stand next to one to appreciate that.

PS - The best thing about the Top Gear Bugatti video is you can actually see the exponential approach to terminal velocity as the spinning of the digital speedo slows down.

PPS - This was started ages ago, but only finished up and posted at the end of December. I'll try to monitor comments to be sure they don't sit too long in the moderation queue.