Help on science project....

[halfracedrift]

hi
http://mrfizzix.com/autoracing/tiresgrip.htm

can anyone explain to me the phytagorean theorem there? i know what it is, but i don't understand why they use it....

quote:
It is a circle centered on an x-y axis graph. The radius of the circle is 1 unit. 1 unit is equal to the adhesion limit of a tire. Thus, on the traction circle, .45-G of acceleration would be .5 graph units, since it is half the tire's limit. The y-axis represents acceleration and braking. The x-axis represents turning. Anyone who has basic geometry can find if the tire will slip or not using the traction circle. basically, if you have graph paper, you can just pinpoint the spot. For example, if you are using 1-G rated tires, and are accelerating at .5-G and are in a 15-m turn at around 20-mph (.5-G of lateral acceleration, see above) your tires should hold. To prove this mathematically, we can use the Pythagorean Theorem. Draw a right triangle with the horizontal leg representing lateral (turning) acceleration, and the vertical leg representing acceleration/braking force. Using the Pythagorean theorem we can find the hypotenuse:

R2 = x2 + y2

R2 = .52 + .52

R2 = .25+.25

R2 = .5

r = .71-units

:end quote :

i don't get it...... ><

 

[Hooligan]

Originally posted by halfracedrift
hi
http://mrfizzix.com/autoracing/tiresgrip.htm

can anyone explain to me the phytagorean theorem there? i know what it is, but i don't understand why they use it....

Let's say you have a circle. Or some other, semi-round object, like an ellipse. You're in the center of it, and you want to draw an arbitrary straight line from the center to any point on the edge (see red line in image). It's kind of hard to figure out the distance to that line, right?

But that line exists on a regular set of coordinates (the crosshatch centered on the circle). This red line doesn't just move in one direction, it moves some distance up, and some distance to the right (blue lines in second image).

We can measure the distance for X and Y, so what is Z? Directions X and Y are like Longitude and Latitude on a map; we have measurements for those North-South and East-West directions. So, for this example, let's assign arbitrary values for X and Y:

X = 2.0 (um, feet...or inches. Depends on what you're measuring).
Y = 2.5

Fortunately, we don't have to come up with any funky equation for this because the Greek mathematician Pythagoras already did this thousands of years ago. It's based on the right-angled triangle: If you know the two sides adjacent to the right angle (X and Y) you can calculate the third side (Z), because all right-angle triangles are the same -- at least in regards to calculating Z. (Note: X is the same, whether at the top or bottom of the triangle. In fact, the triangles created above and below the red line are 100% symmetrical.)

The equation Pythagoras came up with is:

Z^2 = X^2+ Y^2

or, solving for Z (taking the square root of both sides)

Z = (X^2 + Y^2)^0.5

Let's plug in our numbers:

Z = (2.0^2 + 2.5^2)^0.5
Z = (4.0 + 6.25)^0.5
Z = (10.25)^0.5
Z = 3.201...


The reason the pythagorean theorem was used in calculating tire grip is because it's the easiest way to find the total force on the tire. When the car is going straight, picture the red line as perfectly straight up. Easy to determine that value, right? But on a turn -- or better yet, a powerslide -- that line starts to wander around the circle. There's some force to the side, and yet still some force forward. To find what the length of that line is (the total force on the tire), simply draw lines "down" to the X and Y axis (as is done in the first image below). This creates the right-angle triangle, which then allows you to use the pythagorean theorem to find the force on the tire at that point.

http://regentsprep.org/Regents/math/fpyth/Pythag.htm

 

[halfracedrift]

ahhhhhhh i get it.....

using the example from the site, say we're exerting 1 g force on turn right and accelerate
does that mean the tires will NOT grip because the triangle that'd drawn will be OUTSIDE of the circle?

edit: hooligan i'm gonna add you to my list of acknowledgements ok? so is 12 sec civic, cuz you two both helped me..