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# Time, Distance, Speed and Horsepower

Updated: Aug 28, 2012

I catch him in the corners, but he just pulls away from me on the straights... sound familiar ? Let's take a look at some of the reasons that other car seems to get so far ahead on the straightaway.

The racetrack can be the source of some very interesting illusions. One of the most puzzling illusions is the time versus distance illusion:

1) Time Versus Distance

Here's the basis of the time versus distance illusion:  A constant time difference between two cars is a greater distance at greater speeds.

Suppose, for example, that in the middle of a slow corner you get within one car length of the car you're chasing. So, let's say that your car's nose is 20 feet behind the nose of the car ahead. For this example, let the corner speed be 40 mph for the slow spot of the corner. At 40 mph you're covering about 59 feet per second. So, when the nose of your car is 20 feet behind the nose of another car at 40 mph, you're 0.34 seconds behind.

Now, imagine that you accelerate exactly the same as the car ahead, and that you exit with exactly the same cornering speed, keeping exactly 0.34 seconds behind the other car. As you accelerate down the straight, keeping always exactly 0.34 seconds behind, the distance between the two cars increases. For example, if you stay behind that other car by exactly 0.34 seconds, when you reach 110 mph, the cars will be travelling 161 feet per second, and your separation will become 54 feet. It looks like you're falling way behind, but its just an illusion, you're still a constant 0.34 sec behind.

It looks like he is pulling away... but he isn't. The car ahead seems to pull away, but in reality, the time separation has never changed. Just an illusion.

And here's is another example of the illusion that can be mind boggling. Imagine that you are right on the tail, touching the tail of the car in front of you (zero separation) coming out of a 40 mph turn. That means that the nose of your car is about 10 feet behind the nose of the car ahead. So, at that instant, you are 0.17 sec behind the car ahead. Then, if your cars are exactly matched in horsepower and aerodynamics, the car ahead will keep its nose 0.17 sec ahead of you all the way down the next straightaway. At 110 mph that will be a distance of 27 feet. So, it looks like the car ahead pulled away from you.... gees where did he get that horsepower... but in reality, you were a constant 0.17 sec behind. Think time... not distance.

In reality, the drafting effect will reduce the aero drag of the following car more than the leading car, so if you have matched cars, the following car will actually have an advantage, but that's another story...

And speaking of other stories, lets take a look at corner exit speed. For many drivers, one of the toughest issues is corner exit speed. It doesn't take much speed difference at the corner exit to make a big difference in position by the end of the next straightaway.

2) Corner Exit Speed

This one is not an illusion. Corner exit speed is king.

For the following examples, I'll use data from my SCCA Spec Racer Ford (SRF). Based on the performance of a typical spec racer, as documented on my Dyno Test page,  it's possible to calculate the time and distance separation of two identical cars when the only difference is the corner exit speed. I won't bore you with the math, but I use a program called MathCad to perform the calculations.

If two identical cars exit a 2nd gear corner with a 2 mph speed difference, here's what happens as they head down the straightway:

 1000 ft 2000 ft 3000 ft Car 1,   50mph exit speed 8.956 sec, 94 mph 15.639 sec, 108 mph 21.733 sec, 115 mph Car 2,   48 mph exit speed 9.059 sec, 94 mph 15.755 sec, 108 mph 21.856 sec, 115 mph Difference: 0.103 sec,   14 ft 0.116 sec,   18 ft 0.123 sec,   21 ft

As you can see, Car number 2 is at a distinct disadvantage due to only a 2 mph difference in corner exit speed.  At the end of 1000 ft from the corner exit, car number 2,  which had the slower corner exit, is 0.103 seconds behind car number 1. At their speed of 94 mph, that will be a distance of about 14 feet.

On many tracks, this scenario can be repeated many times per lap, leading to lap time differences of up to a second a lap. Just by exiting every corner 2 mph faster.

3) Corner Exit Speed Versus Horsepower

In the previous examples, the cars have been assumed to be identical. But, what would happen if car number 2 had more horsepower?  In the following calculations, Car number 1 has 100 hp and exits the corner at 50 mph. Car number 2 has 102 hp but exits the corner at only 48 mph.

Here's what happens to these two cars as they head down the straightaway:

 1000 ft 2000 ft 3000 ft Car 1,   50mph exit, 100 hp 8.956 sec, 94 mph 15.639 sec, 108 mph 21.733 sec, 115 mph Car 2,   48 mph exit, 102 hp 9.023 sec, 94 mph 15.694 sec, 108 mph 21.775 sec, 115 mph Difference: 0.067 sec,  9 ft 0.055 sec,   9 ft 0.042 sec,   7 ft

From this data, you can see that it takes more than 2 horsepower to make up for just a 2 mph difference in corner exit speed. At the end of 1000' from the corner exit the slower exiting car is still .067 seconds or about 9 feet behind, despite having 2 more horsepower. The additional 2 horsepower is just not enough to catch the car that exited the corner only 2 mph faster.

There are three very important things to learn from this: corner exit speed, corner exit speed, and corner exit speed. And don't forget, an additional 2 horsepower is difficult to get out of this stock engine.

If you could get an additional 5 hp, here's what would happen:

 1000 ft 2000 ft 3000 ft Car 1,   50mph exit, 100 hp 8.956 sec, 94 mph 15.639 sec, 108 mph 21.733 sec, 115 mph Car 2,   48 mph exit, 105 hp 8.970 sec, 95 mph 15.602 sec, 108 mph 21.659 sec, 115 mph Difference: +0.014 sec, + 2 ft +0.037 sec,  + 6 ft +0.075 sec, + 13 ft

From this data, you can see that a slow cornering car would need to have about a 5 horsepower advantage in order to catch up with a more skilled driver who can exit the corners 2 mph faster.

In actuality, the speeds shown above are probably a few mph faster than a spec racer will really achieve, since I have neglected the windage losses in the transmission, and those losses are significant at high speed. However, even if the top speed calculations are off as much as 5 mph, the relative times and distances are still within a few percent of the numbers shown here.

The moral of the story is that a small increase in corner exit speed will have a greater affect than a few more horsepower.

Richard Shelquist