Circumference

[mountainman]

For the geeks..need to know how far a horse running one mile (on a one mile oval) actually travels if remaining 21 feet out from the rail.

[VigorsTheGrey]

For the geeks..need to know how far a horse running one mile (on a one mile oval) actually travels if remaining 21 feet out from the rail.

I don't know the formula but is this to know how far forward to place the starting gate when the dogs go up?

You would have to know the radius of the curves first...

[mountainman]

no, sir

[VigorsTheGrey]

I was wrong about that one, here is the formula:

http://www.csgnetwork.com/circumellipse.html

[upthecreek]

This may be a stupid question,but how do they actually determine where to start a race @ 6F 1 mile etc? Do they use one of the measuring wheels like they use at accident scenes? Do they measure along he rail or? Just curious

[VigorsTheGrey]

many racetracks in the United States are exactly one mile (1,609 m) in circumference; often such racetracks are symmetrical ovals, with both straightaways and both turns being precisely 1⁄4 of a mile (402 m).

[formula_2002]

always wondered why a rectangle has a fixed area, length x width, but once you form a circle using the same length and width segments , the area is infinite, 3.14.....x radius squared. :)

[Elliott Sidewater]

42 times pi or approximately 130 feet

[EMD4ME]

Of all the times cratos should respond, he doesn't :bang: :bang: :D

[formula_2002]

42 times pi or approximately 130 feet
I think it's appox 125 feet

5280 ft= 1 mile
circumference of 1 mile oval = circumference of 1 mile circle

circumference = 2x pi x r

5280= 2 x 3,14 x r
r= 840.764 ft
r = 20' + 840.764 = 860.764
circumference = 2 x 3.14 x 860.764 = 5405.59
5405.59 ft - 5280 ft = 125.59 feet

[Elliott Sidewater]

I think it's appox 125 feet

5280 ft= 1 mile
circumference of 1 mile oval = circumference of 1 mile circle

circumference = 2x pi x r

5280= 2 x 3,14 x r
r= 840.764 ft
r = 20' + 840.764 = 860.764
circumference = 2 x 3.14 x 860.764 = 5405.59
5405.59 ft - 5280 ft = 125.59 feet
I think we have the same answer, because you used 20 ft out from the rail and he said 21 ft.

[formula_2002]

I think we have the same answer, because you used 20 ft out from the rail and he said 21 ft.

my error. you are correct

[cj]

I think you guys are using too high a number. On a one mile track, the circumference of the turns is not one mile. You can eliminate the straight aways as no matter where the rail is placed the distance is the same when running those parts of the course. Only the turns matter.

____
( ____ )

The shape of a track is a called a stadium or discorectangle.

We only care about the () part, so definitely not a mile.

[cj]

So for an example, let us say the straights are 5/16 mile each, or 5/8 in total. That leaves three eighths for the turns, so the perimeter is only 3/8 mile or 1980 feet. That is the part that changes when the rails are out.

[VigorsTheGrey]

All ovals are not the same...in the case of tracks with straight stretches, then you would need to know the length of the peculiar straights and the radius of the curves, mountaineer for example, has differing radii of her curves...

For ovals without straights, you would need to know the length of the major and minor axis, assuming the oval is symmetrical.

[formula_2002]

So for an example, let us say the straights are 5/16 mile each, or 5/8 in total. That leaves three eighths for the turns, so the perimeter is only 3/8 mile or 1980 feet. That is the part that changes when the rails are out.

yes the straightway stay the same length. the turns increase.
total increase is 131' 11 1/2"

see attached

[formula_2002]

All ovals are not the same...in the case of tracks with straight stretches, then you would need to know the length of the peculiar straights and the radius of the curves, mountaineer for example, has differing radii of her curves...

For ovals without straights, you would need to know the length of the major and minor axis, assuming the oval is symmetrical.

regardless, something 1 mile long is 1 mile long, regardless it's shape.
it reminds me of the question, what weighs more a pound of feathers or a pound of concrete?

[VigorsTheGrey]

regardless, something 1 mile long is 1 mile long, regardless it's shape.
it reminds me of the question, what weighs more a pound of feathers or a pound of concrete?

If you lay a string on top of the rail the string would measure 1 mile. If you lay a string on the ground 21 ft from the rail all around, how much longer will this string be than the one along the rail?

I see what you are saying that regardless of the shape of the rail, there is still one to one correspondence of 21 ft out at any given point from the rail.

Yet the strings have different lengths because they have different circumferences....as you know.....what is your point?

[therussmeister]

As long as the turns add up to one complete circle the added distance running 21 feet from the rail is the same regardless of the size of the oval or the radius of the turns.

If you created a race course for mice that is a circle one foot in diameter, and also created a race around the equator of the earth, a mouse running 21 feet from the rail and a airplane flying 21 feet over the equator will each respectively travel the same added distance as their respective competition running along the rail or travelling on the earth' s surface.

[VigorsTheGrey]

As long as the turns add up to one complete circle the added distance running 21 feet from the rail is the same regardless of the size of the oval or the radius of the turns.

If you created a race course for mice that is a circle one foot in diameter, and also created a race around the equator of the earth, a mouse running 21 feet from the rail and a airplane flying 21 feet over the equator will each respectively travel the same added distance as their respective competition running along the rail or travelling on the earth' s surface.

Yes, but I thought what was being asked was an answer that had a peculiar foot and inches answer.....for that one needs to know the specific layout of a particular track, straight away lengths, and curve radii lengths....and if it is a true oval, it is not the same equation...

[bobphilo]

For the geeks..need to know how far a horse running one mile (on a one mile oval) actually travels if remaining 21 feet out from the rail.
Circumference of a circle = (2x radius) x 3.14
(2x21)x3.14 = 132

Since each turn is 1/2 the circumference of the circle formed by both turns, adding 21 feet to the radius adds 66 feet to the turn. The size of the track is irrelevant.

Ainslie describes this in his "The Complete Horseplayer".

[bobphilo]

always wondered why a rectangle has a fixed area, length x width, but once you form a circle using the same length and width segments , the area is infinite, 3.14.....x radius squared. :)
That raises the problem of irrational magnitudes like Pi. In Ancient Greece Pythagoras condemned to death any of his followers that disclosed this since his Philosophy was based on the premise that the world was made up of rational numbers.

[bobphilo]

As long as the turns add up to one complete circle the added distance running 21 feet from the rail is the same regardless of the size of the oval or the radius of the turns.

If you created a race course for mice that is a circle one foot in diameter, and also created a race around the equator of the earth, a mouse running 21 feet from the rail and a airplane flying 21 feet over the equator will each respectively travel the same added distance as their respective competition running along the rail or travelling on the earth' s surface.
Correct. That's reason the increase in ground on any turn where the radius is increased by 21 feet is 66 feet as I describe in my post.
The straightaways play no part in ground loss.

[VigorsTheGrey]

Circumference of a circle = (2x radius) x 3.14
(2x21)x3.14 = 132

Since each turn is 1/2 the circumference of the circle formed by both turns, adding 21 feet to the radius adds 66 feet to the turn. The size of the track is irrelevant.

Ainslie describes this in his "The Complete Horseplayer".

This is an oval not a circle....does the shape make a difference in the equation?

[bobphilo]

This is an oval not a circle....does the shape make a difference in the equation?

Doesn't matter. The turns form a circle. The straightaways play no part in ground loss on the turns.

[cj]

This is an oval not a circle....does the shape make a difference in the equation?


It isn't an oval, it is a stadium as I mentioned earlier.

[formula_2002]

Circumference of a circle = (2x radius) x 3.14
(2x21)x3.14 = 132

Since each turn is 1/2 the circumference of the circle formed by both turns, adding 21 feet to the radius adds 66 feet to the turn. The size of the track is irrelevant.

Ainslie describes this in his "The Complete Horseplayer".

Neat.

[VigorsTheGrey]

It isn't an oval, it is a stadium as I mentioned earlier.

Sorry, I just assumed oval because mountain man started thread stating oval and I did not see a reposting by him to confirm stadium...however, we now see the oval and stadium are moot since straight portions don't change add to the increased distance...

[cj]

Sorry, I just assumed oval because mountain man started thread stating oval and I did not see a reposting by him to confirm stadium...

I also just like saying stadium and discorectangle.

[EMD4ME]

I also just like saying stadium and discorectangle.

I think he needs to imbibe the proper vocabulary usage. :lol: :lol: :D :D

But he means well. A good soul!

[VigorsTheGrey]

I also just like saying stadium and discorectangle.

Thanks for the new words.....never heard stadium used in that meaning and discorectangle is new to me as well

[formula_2002]

yes the straightway stay the same length. the turns increase.
total increase is 131' 11 1/2"

see attached


to be clear

[bobphilo]

For the geeks..need to know how far a horse running one mile (on a one mile oval) actually travels if remaining 21 feet out from the rail.

Mountainman, an answer to your question was submitted to be 66 feet based on the mathematical formula. Was this not useful to you? Hope I was not just wasting my time in this.

[Cratos]

Mountainman, an answer to your question was submitted to be 66 feet based on the mathematical formula. Was this not useful to you? Hope I was not just wasting my time in this.
130.54 feet is correct

[bobphilo]

130.54 feet is correct
Not so. Please consult the equation relating the radius of a circle to the circumference of a semi-circle not a full circle. You forget that mountainman was referring to the ground loss on 1 turn (a semicircle not a full circle) which would be about 66 feet.

Actually it doesn't really matter since Mountainman is not acknowledging any answer to his question. Hopefully anyone else interested is getting something out of this.

[bobphilo]

yes the straightway stay the same length. the turns increase.
total increase is 131' 11 1/2"

see attached
Formula_2002, you are looking at the total ground loss over 2 turns. Each turn is a semi-circle so the ground loss on each turn is half of that or about 66 feet.

[Lemon Drop Husker]

The shape of a track is a called a stadium or discorectangle.

Discorectangle?

If that is the case, then why isn't the Saturday Night Fever soundtrack playing full time at every track across the country?

https://www.youtube.com/watch?v=u6prBr1jY24

[Cratos]

Not so. Please consult the equation relating the radius of a circle to the circumference of a semi-circle not a full circle. You forget that mountainman was referring to the ground loss on 1 turn (a semicircle not a full circle) which would be about 66 feet.

Actually it doesn't really matter since Mountainman is not acknowledging any answer to his question. Hopefully anyone else interested is getting something out of this.

My apologies, I read it as 2 turns, but if it is a one turn track; the number would be 65.27 feet

[bobphilo]

My apologies, I read it as 2 turns, but if it is a one turn track; the number would be 65.27 feet
No problem. :ThmbUp:
Actually to be fair to you, the question was a bit ambiguous. At some tracks mile races are run out of a chute around only one turn and the ground loss would be about 66 feet. If they are run around two turns then the your figure of about 133 feet of total ground loss applies.