# Cars Versus Horse on Dirt Track

1. May 27, 2004

### mbentley

[SOLVED] Cars Versus Horse on Dirt Track

Ok,

A little off topic, but something my co-workers and I have been arguing about. They believe if i were to race against horses on an equestrian track in my 240 horsepower 3000lb car, the horses would beat me. With their very un-educated understanding of physics they claim I would not have enough traction on the soft dirt corse and that the horses would out corner me as well. Cornering is pretty much up to the driver, but I'm skilled at dirt track racing myself so I believe we can throw that out the door as I dont need traction to make a 180 degree turn at high speeds.

On their theory of me not having as much traction, I believe the contrary. I would have 4 tires specifically designed to improve traction with much more surface area on the ground compaired to the horses relatively low surface area.

The thing im having problems with is the fact that my in my formula I have rotational mass unlike the horses.

So, I wanted to get some scientific / not so scientific reasons why either the horses or I would win. Does anyone care to waste brain power on this one? Please email me if you have some input.

Thank you,
Michael Bentley
BentleyPC.com

2. May 27, 2004

### NateTG

The first problem is that you haven't specified anything useful about the track.

There are a couple of competing limiting factors:
Power
Traction

On a dirt track, a horse is going to have better tracktion (since the hooves can dig in) but horses have less power. So, while the limiting factor is traction, the horse will beat the car. If the limiting factor is power, then the car is going to blow the horse away.

Also, poor driving (which I'm assuming is not a factor) is almost guaranteed to lose the car the race since the car can:
1. Peel out and get stuck
2. Loose control on the curves (which are high-acceleration areas)

3. May 27, 2004

### KingNothing

NateTG, no offense, and I can't make this claim for certain, but that seemed like the same argument that his coworkers were (on a slightly more general level) making.

Let's get some number in here.

The kentucky derby is 1.25 miles long, and the speed record is 2 minutes (actually 1 minute, 59 and 2/5 seconds).

Going 1.25 miles in 1/30 of an hour si the average speed of 37.5 mph.
Now, your average good racing car can go around a cement track at, lets say, 130 mph. Since we are talking about a decent car, I wouldn't put 85 past it on a cement track.

Now, assuming the traction problem isn't such that it would double the time, (thats a HUGE friction difference, i dont think its reasonable)....the car would win.

Edit: Now, the coefficient of rubber on dry concrete is about 1.0. It says in my physics book, anyway. The coefficient of a car tire on grass is about .35 http://hypertextbook.com/physics/mechanics/friction/ [Broken] kinetic...so I'm guessing like 0.6 or more static (total guess). Well, I dunno. I think the coefficient of a car tire on cement is prolly less than 1.0. Somewhere around 0.9 maybe. Anyhoo, assuming the coeeficient of grass vs. dirt isnt that far off, not more than a few tenths, I don't think it would be enough to take the car out of it. Besides, the car will go faster on the straighter parts anyway, so if it can even manage, say, 30 around the curve, it's prolly still gonna win.

Last edited by a moderator: May 1, 2017
4. May 27, 2004

### mbentley

youre exaclty right. I remembered this on the long drive home from the office. My coworkers frequent various animal tracks often. They seem to know a bit about the surface too. Apparently there is a several layers of the dirt. 1st being a soft layer, then medium so the horses can dig in and finally a impermeable layer. I believe if i were not to peel out, I would be able to hold traction well with the 2nd and 3rd layers.

Even in a few inches of water, during rainy conditions on asphalt, we can expect most cars to be able to maintain traction up to say 45 mph. However, I am unsure as to the frictional properties of both water and soft dirt.

So I am perplexed...

5. May 27, 2004

### mbentley

Given KingNothing's research into the subject, I am certainly sure the car would win.

6. May 27, 2004

### franznietzsche

Not being off by more than a few tenths gives a range of 0.05-0.65...i'm hoping you meant hundreths, because the difference in either direction would be HUGE.

7. May 27, 2004

### KingNothing

I said the right thing, I just didn't say it very well...I didn't mean tenth places, I meant that the real value prolly isnt much different than about plus or minus one tenth of 3.5 plus .35. That is "not more than a few tenths of 0.35 off"...so our range would be about 0.245 to 0.455. Sorry for the confusion, it's jsut kinda how we talk where I come from.

8. May 27, 2004

### Njorl

If you have a jeep, you will blow the horses away. If you have a Ferrarri, you'd do better to get out and run.

I don't know if any 2-wheel drive car could move on a horse track. Rear wheel drive would be no good. It isn't a question of getting traction on dirt. Your tires will get plenty of friction. It is just much easier to toss the dirt backwards then to move the car forwards.

Njorl

9. May 28, 2004

### KingNothing

That's basically what we mean when we say traction....generally thats taken into account and 'traction' is just an encompassment of all the things making it easier or harder for your car to accelerate on a given surface...

I may be wrong, but I doubt it, no offense...this is jsut waht I mean when I say traction. There's a good chance that it's basically what other people mean too.

You also have to take into account that the person driving isn't just going to floor it when the race starts...the driver is smarter than that. We have a race track in my town that is all dirt...we have races pretty regularly on it. I think it's 1 mile around....and it takes a driver maybe 45 seconds to get around if that. It's not the same kind of dirt, but I think it's a reasonable comparison.

10. May 28, 2004

### ray b

back in the early days most car races ran on dirt horse tracks because they were there
some dirt tracks are still used in races for both cars and motorcycles

a horse will beat a car over the first hundred feet

11. May 28, 2004

### NateTG

Note that I did not claim that the car would loose, only that it's a competition between traction and power.

Let's assume that we're talking about a straight drag race and that friction is the only limiting factor:
Then $$\sqrt{\frac{2d}{a}}=t$$ so we have that the time is proportional to $$\frac{1}{\sqrt{\mu_s}}$$.
Now, let's take a look at your numbers.
$$\frac{1}{\sqrt{1}}=1$$
$$\frac{1}{\sqrt{.35}}\approx 1.7$$
so changing from concrete to grass will, in fact, almost double the time. (Wet grass is probably a full doubling.)

Now
Let's approximate a mile and a quarter as 2000 meters (this is fairily close), and let's say, for now that the horse is going to make 120 seconds.
So we can figure out the minimum (average) acceleration to beat the horse is roughly $$.3 \frac{m}{s^2}$$. Since the track is an oval, the number is probably closer to twice that, so we're looking at $$\mu_k \appox .05$$ as the threshold value for determining whether the car beats the horse assuming the derby is a single lap race.

As the laps get shorter, the necessary acceleration gets higher. If we assume that the horse manages to get 24 second quarters on a quarter-mile track, then the car is going to have real trouble beating it barring some specialized tires.