My son, my dad, and I went to the 12-hours of Sebring race yesterday! It was a great time... perfect weather and lots to see and do and experience. Oh, and there was a car race as well :-) The Audi R8 has owned this race for years! The above isn't the actual car that won, but the same model. It beat out Corvette CR-6s, the new Aston Martin DBR9s, Porsche 911s, Maserati MC12s, Lola EX257s, Saleen S7Rs, Dodge Vipers, Ferrari 550 Maranellos, and others,  After 6 years, Audi will debut the R10 next year, which should secure the gold for another generation.

If you haven't been to a car race before (I must be one of the few that hadn't), Sebring is the first and longest race in the annual American Le Mans Series. It's a "street race" (unlike Daytona's NASCAR style) on a 3.7 mile loop on an old WWII airfield with flat hairpin corners that require strategic down shifting and braking. The longest straight segment allows cars to approach 200mph! Average lap speed can exceed 120mph. This year 37 cars started (and 18 finished) the 300+ lap race. Each car has a pit crew and several drivers. There are four classes of cars (each capable of different top and cornering speeds) racing together, making it a very different race than, say, the Indy 500.

Like a golf tournament, there are 4 days of racing (Wed-Sat) leading up to Saturday's main event. Many thousands of people lined up on Wednesday to drive their RVs and U-Haul trucks and School Buses and other interesting forms of transport onto the grounds for an extended campout/party. Some built scaffolding along the course on which they placed sofas! It's March after all - Spring Break time. People watching was as entertaining as the race itself! A friend of mine has gone every year since 1959.

There were also many interesting "sponsor" displays, including race cars in various stages of (de)construction, allowing fascinating views of the internals of the cars.

As we watched the cars fly by our viewing area (we set up our canopy and chairs on a grassy knoll between turns 6 and 7), my dad and I discussed the stresses involved in engines that propel these cars ~1300 miles at an average speed of well over 100 mph, much of it accelerating out of a total of over 4000 turns over 12 solid hours. Each piston cycles about 5 million times! We wondered, at red line speed, how fast those pistons move (12 hours is a long time to talk :-). Are those piston heads traveling faster (inside the cylinder) than the car itself? Reflecting on riding my bike at 20mph, I knew my feet (acting like a piston) don't move that fast... so I guessed that car pistons at red line would move slower than a car's top speed.

Well, I had to figure it out. The math is easy. Obviously piston speed is tied to RPM and Stroke Length, and just indirectly related to the car's forward motion (you can spin the engine in neutral at a standstill). At one of the displays I found out that the typical stroke length for these types of engines is 2.5-3.5 inches, and the typical red line is 8,000-10,000 RPM. Note that RPM measures the crankshaft rotation rate, not the camshaft, which is rotating at half that speed, as shown in this animated GIF:

Since speed is distance/time, and since the piston head travels 2*StrokeLength (up and down) for each cycle, the *average* piston speed is:

Therefore, a car traveling at nearly 200 mph, at the engine's red line, will have pistons traveling at an average of only around 51mph! I was right.

But wait... that piston starts and stops 18,000 times every minute, accelerating to the next stop just 3 inches away (at a huge "G" force). Average speed does not really answer the question. I had to figure out the peak piston speed. Since it literally explodes from a dead stop (it's a combustion engine after all), possibly the peak speed exceeds the speed of the car?

It turns out that the peak speed equation is complex, with sin/cos kinds of rotational acceleration factors. I took the easy way and looked up stats from several types of race car engines using Google. The ratio of peak to average piston speed is consistently very close to 1.6:1.  So at Sebring, the pistons never traveled faster than about 82 mph.

Even a Formula 1 (NASCAR) car, with an engine that can red line at 19,000 RPM, that has a stroke length of about 1.65 inches and a top speed ~240 mph, will have pistons that average: 2*19000*1.65 = 60mph, and peak at: 95mph. See footnote below.

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http://lordcaffeine.com/wordpress/index.php?cat=2
At 19,000 rpm, 316.7 revolutions and 1,583.3 ignitions take place each second in the BMW F1 engine. 9,500 engine speed measurements are made, the pistons cover a distance of 25 metres, and 550 litres of air are drawn in. In the P84, maximum piston acceleration was 10,000g. Peak piston speed was 40 metres per second.

March 21, 2005 08:10 AM EST Permalink