Tuesday, April 27, 2010

Talladega pas de deux: why restrictor plates necessitate contact drafting

The official Talladega mascot:

Pas de Deux (pronounced as "pah-day-due"), Part 2
Restrictor plates necessitate contact drafting

Engine horsepower is not a single number, but rather a function of speed (engine RPM) and typically has a humped shape; power output increases with engine speed up to a peak and then drops off.

The actual horse power numbers for any given engine and differential gear ratio are a closely guarded secret by each shop. Even though we've seen the actual numbers this is a confidentiality we're not about to breach here so we'll show hp qualitatively (no numbers) but accurately.

A car must be pushed to ram it through the air; the required push (a force) increases proportionally with the square of speed, that is: Force, F = n x (speed x speed).

This diagram shows the pressure on and around a car going 190 mph, high pressure on the front of the car, low pressure behind it.
 Those pressures applied over the frontal area of the car determine the aerodynamic drag.  (Red is high pressure, blue is low pressure)

It is often informative to also look at the pressures on the surface of the car as well.

The power consumption (force x speed) due to aero drag increases with the cube of speed, that is: (speed x speed x speed), so it increases dramatically with speed, and it just keeps on going up. At 190 mph the force required to ram a NASCAR Cup car through the air is on the order of 700 lbs or more.

The net power (engine less aero drag) describes what is left for accelerating the car.

A plot of the difference between the two curves illustrates the frustration of drivers with restrictor plate racing, when the two curves cross there is zero left to accelerate the car and when the net power gets to zero that's as fast as the car will go.

 Note also as the car approaches its terminal speed, the available power for acceleration is also approaching zero, i.e., the car becomes more and more "sluggish," it has no "throttle response," you push the accelerator pedle farther down but the car doesn't go any faster.

The only way to go faster is to reduce aerodynamic drag, hence, the newly realized pas de deux of two cars running nose to tail, literally touching and both cars together ramming the combined block through the air. Notice that the high pressure area on the nose of the second car fills in the low pressure void behind the lead car.

The result is to reduce the overall drag of the two cars together.

Even though the two cars together are not a smooth shape as one can see with the turbulence over the back of the lead car and on the front of the second car, but the combination of two cars pushing together has twice the horse power of one.

Moreover, the two cars have much less drag than the sum of two individual cars, about 27% less drag as shown in these studies.

As a result of the lower aerodynamic drag the speed at which the net power for accelerating the car is zero has increased in the pas de deux, contact drafting.   Thus, two cars together go motoring right by a single car or a long string of cars.

While one might think that if two are good, then three should be better, but the dynamics of getting three cars actually touching nose to tail doesn't work. It is physically impossible to keep the front and back contact forces on the middle car centered for any period of time as the cars do bounce around more than a little. Even though the Talladega track is one of the smoothest tracks on the NASCAR circuit, the cars are not on rails and they move relative to each other. As soon as the forces on the middle car are not centered it turns the middle car around. Thus, three cars trying to run as a trio ends up either being two in a pas de deux plus a third as a trailer, or all three do get together and it's called a wreck.

A surprisingly small gap between the cars is sufficient to mitigate the drag reduction compared to two cars in contact with each other. The pas de deux with a trailer just isn't as streamlined as two.

Don't expect to see too much of the pas de deux formation at the Daytona race in July because the Daytona track is much rougher than Talladega so it is much more difficult to keep two cars in actual contact,…but I bet they'll try. With the repaving at Daytona now scheduled to be completed for the 2011 races it may then make DIS the second pas de deux track, sort of a pas de deux of pas de deux racing.

Next week will be the opposite end of the spectrum of tracks, Richmond, where the turns are the tightest (365' radius), except for Martinsville (188' radius), and the banking at 14 degrees is less than half that of Talladega; the race at Richmond is all about brakes and the right gear to accelerate. This is the track where the race car engineers get to show their skills, it's all in the set-up.

Again, these CFD studies in SolidWorks by FastTrack Racing Challenges for participating junior high and high school teams are possible due to the generous support of SolidWorks (visit their web site and look at the full software package at SolidWorks.com) and in particular thanks to Marie Planchard, their director of worldwide education markets.

Monday, April 26, 2010

Talladega Pas de Deux: why two is the magic number at 'Dega

The official Talladega mascot should be:

Pas de Deux (pronounced as "pah-day-due")

Merriam Webster dictionary defines "pas de deux" as

1. a dance or figure for two performers

2. an intricate relationship or activity involving two parties or things

A funny thing happened in Alabama on Sunday. Suddenly for the first time in memory two cars in a pas de deux outran an entire string of cars at "the big track." Until now a long string of cars-- 5, 10, 15 or more cars-- always had the advantage,…a huge advantage because a string of cars always had less overall drag than one or two alone. But on Sunday suddenly we saw two cars outrunning the freight train; how is that possible when it never worked before?

As many TV commentators remarked repeatedly, "the closing rate of the two cars over the rest of the field is incredible," as much as 15 mph or 22 ft per second, a car length per second. When you're only 3 feet away from another car, they're going 180 mph and you're doing 195, closing on them at 22 ft per second makes the slower car appear as if it is sitting still.

Several factors explain the two car run away: Talladega was repaved in 2006 and the surface is unusually smooth, allowing cars to get very close to each, nose to tail, and stay that way for long periods of time. The geometry of the CoT has the nose and tail of the car at essentially the same height so the trailing car can literally push up against the lead car and shove it. Previously with the car dubbed the Twisted Sister if the trailing car pushed this hard on the lead car they'd lift the rear wheels of the lead car off the ground and they'd both wreck.

Also the CoT with a spoiler on it has a very different wake than with the wing (red is highest speed air flow down to blue which is the lowest speed air flow).

There's a very distinctly larger area of low speed wake behind the race car with the spoiler compared to the race car with the wing. The result is that the two cars can actually touch and stay in contact which reduces the overall drag of the two car duet, considerably, by perhaps as much as 30%.

Power consumption increases with the cube of speed (speed x speed x speed) so the observed difference of two cars together at 195 mph vs one car or a string of cars at 180 mph should have required (7.415/5.832) 27% more power to go that much faster, but actually what happens is that the two cars linked together in a pas de deux have 27% less drag as shown in these studies.

While the two cars have a huge speed advantage there is very little air flow reaching the front of the trailing car, which means that the engine of the trailing car will quickly overheat because cool fresh air is not getting into the radiator. This limits how long the two cars can continue their pas de deux, and from watching the race one would deduce that a couple of minutes is about as long as two cars can stay in contact (NASCAR Cup cars can run 2.2 laps at Talladega in two minutes).

Harvick played the final lap pas de deux perfectly, and then at the last possible moment swung around his dance partner (McMurray) to win the race by a mere 0.011 seconds.

After the race Jamie McMurray was quoted, saying, "it's hard to explain to you guys that aren't in cars, but when there's someone directly behind you and they pull their car out of line really fast, it's like you pull a parachute in your car. It literally feels like you lose 3 or 5 mph immediately, and when that happens, the car that's doing the passing just has the momentum."

It doesn't just feel like the car slows down, it actually does slow down. The aerodynamic drag on a car is the difference in pressure on the front of the car, minus the pressure on the back of the car, and that difference of pressure applied over the frontal area of the car is the drag force (pressure multiplied by area equals force), perhaps 700 lbs or so on a car going 190 mph.

When the cars are nose to tail the low pressure area behind the lead car is filled in by the high pressure area on the front of the second car.

But when the trailing car gets out of line to go around the lead car, suddenly there's a low pressure area behind the lead car and the drag force on the front car suddenly increases by as much as 400 lbs. This has the same effect as throwing an anchor out, it slows the lead car by as much as 5 mph almost instantly.

These CFD studies in SolidWorks by FastTrack Racing Challenges for participating junior high and high school teams are possible due to the generous support of SolidWorks (visit their web site and look at the full software package at SolidWorks dot com) and in particular thanks to Marie Planchard, their director of worldwide education markets.