Brain in Gear - No Need For Speed

When I was a kid, and contrary to most kids my age, I never liked car or motercycle races. I did not see the point : the fastes car would win, right ?

Of course, that is not the case. A couple of other factors come into play. On a circuit with long straight stretches, the car with the highest top speed my have the advantage, while on a circuit with a lot of turns and curves, the car with the best acceleration might be better off. The nerves of the driver matter, too. Go for the brakes a bit sooner than your apponent, and you're left behind. And probably there's some other things : steermanship, tactical insight, overview, knowing when the moment is right to overtake, or not.

Fans of car races know these things far better then I ever will. I'm still not a fan. I do know a thing or two about physics and mathematics, and it turns out that those things may just lety you win a car race, even if the car you're driving is less powerfull and more slow than the others. Revenge of the geeks ?

To show what I mean, you need to understand that forces and speed, in physics, can be represented by arrows. They're called vectors. Vectors are arrows with a starting point, a direction, and a length. In physics, the length and direction can be made to represent the speed of an object. The faster the object, the longer the arrow. And the arrow points in to the direction the object is moving. In the following picture, you see 2 cars going in the same direction, at the same speed (Va = Vb). V stands for velocity, which means 'speed'.

In Mathematics, vectors can be added up, just as speeds can be added up or distracted. This is done by creating parrallellograms. And this works both ways : if you can say that 5+1 = 6, you can also say that 6 = 5 + 1. And you can say that 6 = 4 + 2. Or 6 = 3 + 3. Same with vectors : you can break them down in composing vectors, as in the following picture.

The length of the arrow indicates 'how fast'. The blue arrow is the speed of the car as it is driven by the engine. The orange arrow represents the sideways movement (Vs)

Now, consider two cars, running at approximately the same speed, in the same direction. You're car is less powerfull, so you can expect the other one any time now to speed up and leave you behind. What you need to do it to force him to slow down.

To force your opponent to slow down, you may try to get in front of him, and hit the breaks yourself, so that the other driver has to hit the breaks too. Downside of this approach : you both slow down more ore less equally : you'll still be going the same speed, just slower, and as the other care is more powerfull, it can accelerate faster than you can, overtake you, and leave you behind. What you need is a way to make him slow down, while you keep the same speed, so that he falls behind and needs all that extra power to try and catch up again. Do this at the right moment and you win. But how do you do that ?

Enter the vector ... Say you'd steer your care in front of the other one, at an angle. Probably this is considered unfair, unless you do it at the right spot so that you can claim you were just following the ideal line to steer into a curve. Consider the speed of your car as the sum of 2 speeds : forward (Vf - following the road) and sideways (towards the comlpeting car : Vs). The sum of these two 'components' is still equal to the actual speed V of your car (blue arrow).

Note how the actual 'forward speed', the speed following the road, reduces while the actual speed of your car remains the same : the green vector (Vf a) is shorter that the blue one (Va). That's because some of that speed is being used to go sideways.

The competing car, however, will need to slow down : he'll have to reduce his speed till it's equal or smaller than your forward speed (Vb = Vfa). Or he'd just hit you, but that's not the idea. Since speed is represented by vectors, you can tell by the drawning that he has to reduce his speed. Pythagoras may help you calculate exactly how much (depending on the original speed and the angle at with you approach the car).

What about your car ?
The blue vector represents the actual speed of your car, and shows that this is still the original speed at which you were driving before you executed this maneuvre. As soon as you line up your car, you're again running down that road at that same speed. Maybe a bit less, because the friction caused by the angles of the wheels while making the maneuvre will have slowed you down a tiny bit, but that does not matter. You're now running significantly faster than your competitor, who 'll need all his power just to catch up again.

Quod erat demonstrandum.

(c) Useless Publications Unlimited - subject to disclaimer - More stuff like this  >>
a message from our sponsor : -