A complete waste of fuel

It's been months since I posted anything here, my blog muse having deserted me. However, my interest in energy and related matters has not abated and my reading has kept pace. It's been over nine years since I started driving to, as best I could, minimize fuel consumption and coming up on eight years in April since I started this blog.

But, despite my interest in driving in an economical way and my Lexus CT200h hybrid car, much of my lifestyle demonstrates an excessive use of energy. Among other examples, I'd offer my airplane, my five or six airline round trips (typically to the east coast and beyond) each year, my family's consumerism, and my involvement in the building industry.

But none of that is quite as extravagant as my interest in NHRA drag racing, particularly the "fuel" categories as they're known, those that burn nitromethane (CH₃NO₂) in their cylinders. These vehicles are fascinating to me, they travel 1000 feet (it used to be a quarter mile, but following the death of Scott Kalitta in 2008 it was shortened) in under four seconds, accelerating to well over 300 m.p.h. Attending such an event in person is a sensory overload not to be missed, you feel the sound from the inside out more than you hear it.

A fueler ("top fuel" and "funny car" are the class names for the nitro burning vehicles) will burn almost five gallons of nitromethane in a 1000 foot run. It will burn about 20 gallons in a round, including startup, warmup, burnout, staging, and the actual run. At full throttle, the engine will use about 1.2 gallons/second. More fun facts about top fuel dragsters can be found here.

A race (weather permitting) will run from Thursday through Sunday with qualifying on Friday and Saturday, and a driver may race four qualifying runs, and, should he or she make it to the final elimination from the field of 16, he or she will race four times on Sunday. So, a successful fuel vehicle will make something like 8 runs down the track at an event, burning maybe 160 gallons of nitromethane. Because it's an elimination format on Sunday, the 16 qualifiers in each of the fuel classes will run a total of 15 two car races, so a maximum of 600 gallons of nitro is burned. The qualifying will add 1,440 gallons or so for a total of 2,040 gallons for the event. Of course, this is quite variable, depending on weather, mechanical breakdown, number of entrants, etc.

I've been scouring the web for video of a top fuel race taken in such a way that I can use the fantastic (and free) Tracker Video Analysis and Modeling Tool (did I mention that it's free?). Such a video would shoot, as much as possible, from a still platform with a wide lens and a line of sight perpendicular to the track. Aerial would be great too, if it met those conditions. So far, no such luck.

The reason I'd like to find it is that I'm curious as to the actual acceleration and the power delivered by the tires to the track. Failing the video, I've found a couple of sources for time, distance, and speed in half-second increments (plus the 0.35 second increment from 3.5 seconds to the finish at 3.85 seconds and 1000 feet. I can get some estimates from those.

Putting the eight data points into Mathematica and generating a linear third order polynomial fit (for a polynomial, it has to be at least third order or else acceleration, the second derivative of displacement, would be constant, something that's clearly not the case), and then finding the derivative (acceleration), it looks like the Grubnic's dragster is accelerating at about 4.5 Gs at 1 second. As a sanity check, distance traveled ~s= \frac{1}{2} a t^{2}~ where ~a~ is average acceleration over the distance (and assuming initial conditions of 0 distance and 0 speed), so average acceleration ~a=2s/ t^{2}~. Substituting 1000 feet for ~s~ and 3.85 seconds for ~t~, ~a~ is about 135 feet/second², or about 4.2 Gs. At 0.25 seconds, it looks like acceleration is in the vicinity of 5.2 Gs.

Given that a top fuel dragster weighs about 2320 pounds, we can determine the power applied by the tires to the track. We can find the force from the mass and acceleration. Let's use the situation at one second. We have a mass of 1052 kg accelerating at 43.98 ~m/s^{2}~, so the force is 46,285 Nt. Since force*speed is power, and the vehicle is moving at 53.82 meters per second, we can estimate that about 2.5 megawatts represents the rate that the tires are performing work. This is about 3,340 horsepower. It's stated on various web sites that the engines generate between 8,000 and 10,000 horsepower. As far as I know, a top fuel nitromethane burning engine hasn't been tested on a dynamometer. I've seen statements that no dynamometer exists that can measure that level of power, but I believe that such instruments do exist. I think the problem is that the engines can't survive at full power long enough to achieve accurate measurements.

As to the difference between, say, 8,500 and 3,340, a lot is lost in the clutch system, and it takes at least 700 horsepower just to drive the supercharger. Further, in the use of ~f=ma~, it's actually ~ \Sigma f=ma~ where ~\Sigma f~ is the sum of forces on the vehicle. Most significantly, I didn't include aerodynamic drag or tire rolling resistance, both of which will be quite significant with tire pressure at around 7 p.s.i.g. and speed in the 100 m.p.h. range. Given that the exhaust and the wing both produce down force (enabling traction at higher power than would otherwise be possible) and the low modulus of the tires resulting in huge hysteresis, rolling resistance is likely to be a more significant component of overall net force against the acceleration than is true in street cars.  Further, at higher speeds, the drag of the vehicle is very high, in particular due to the induced drag generated by the wing at the rear of the vehicle. Thus, the force applied by the tires to the track must not only overcome the inertial mass of the vehicle, it must overcome aerodynamic drag and rolling resistance. Thus, engine horsepower in the 8,500 or even 10,000 horsepower range seems quite plausible.

Now, I strongly suspect that it's much more complicated than that, particularly in the first second or so. Sadly, the inability to find a video that I can analyze makes it impossible to do any better, but I'll keep on the lookout.

I've typically wrapped up posts with a song, but a top fuel dragster makes a music all its own.




Ps: I'll be curious to see if any of the denizens of Guy McPherson's "Nature Bats Last" Near Term Human Extinction community, with whom I've been engaged in some back and forth lately, wanders back to my blog. A couple did so earlier and noted that I'm not a climate scientist, I'm pretty sure this topic will convince them to discount me completely (if they haven't already done so). On the other hand, this post may fit well with the McPherson/doomer/"we're special because we know that we're all doomed and you don't" crowd. After all, as they see it, nothing (to be read literally as "no thing") we do can help, what difference can it make if we burn some rubber and nitromethane?