Dude, You're Throwing HEAT!March 11, 2010 11:23 AM   Subscribe

How fast would you have to throw a baseball in order for it to catch fire?

I want a number for fiction purposes.

Stipulations:

* We are imagining that the ball will be "thrown" by magic, not by some existing technology or real-world process that has built-in limitations. It's just gonna go zoom!

* We will go from room temp (defined here 22 Celsius / 72 Fahrenheit) to "temperature X" in the space of 60 feet, 6 inches (or a reasonably close estimated distance). This is the distance from a baseball mound (actually, the rubber) to the front edge of home plate.

* The event will occur at sea level, at 22 Celsius / 72 Fahrenheit. But for our imaginary purposes, humidity or other atmospheric effects should be ignored.

* By "catch fire," I mean, the surface of the ball is raised to the temperature at which leather is generally known to ignite, which according to this page, is 212 Celsius / 413 Fahrenheit. For our imaginary purposes, we'll assume there is sufficient oxygen for the ball to spontaneously "catch fire" at this temperature.

Have at it, physics nerds!
posted by Cool Papa Bell to Science & Nature (19 answers total) 14 users marked this as a favorite

Response by poster: Oh, one more thing ... unless you have a way to answer the question of at what point the cover is stripped off the ball at such high speeds, let's assume that our imaginary ball remains intact during its trip to the plate.
posted by Cool Papa Bell at 11:31 AM on March 11, 2010

The physics nerds will need to consider time as well as speed. To reach 212 degrees C, the friction (which is a function of the speed) will need to be applied for a certain amount of time. Given the short distance and the high speeds you're thinking of, there may not be enough time for the heat to accumulate without bending some other consequences such as the air turning to plasma around the ball.
posted by alms at 11:34 AM on March 11, 2010

I think the answer is "It won't." Not under that set of facts. Sixty feet isn't enough room.

The terminal velocity of a baseball is about 95 miles an hour. That's as fast as a baseball will travel through the Earth's atmosphere near sea level at 1G of acceleration. As it won't burn up under those circumstances, you need a lot more speed.

If you drop a baseball from orbit, yeah, it'll burn up before it hits the ground. The X-15 experimental "rocket plane" got to over 2000 miles per hour and reached temperatures of 400F, so that's probably in the range we're talking about. Call it an even 1000 miles an hour, just for shits and grins.

The problem is that to get that speed you need acceleration. And accelerating the ball to thousands of miles an hour is going to take either massive acceleration to achieve in sixty feet, destroying the baseball before it ever has a chance to catch fire, or take way longer than the space you've given us. Either that or you can start outside the atmosphere with a far higher starting velocity, but that isn't the same sort of game anymore.

I can't think of even a magic device which could accelerate a baseball to a high enough speed to catch fire while preserving the ball as a ball in that small a distance.
posted by valkyryn at 11:54 AM on March 11, 2010 [1 favorite]

I'd complain about not previewing, but I think I answered the question anyways. About 1000 miles an hour, give or take a few hundred.
posted by valkyryn at 11:55 AM on March 11, 2010

specific heat of leather = 1.5 kJ/kg K; density = 0.8 g/cm^3.
you're heating the front surface of the ball, which weighs (7.3 cm diameter, half the surface of that sphere, assuming a thickness of 3 mm) 20 g.
you'd need 190 K * 0.020 * 1.5 = 5.7 kJ of heat to raise the surface to ignition temp.
A 145 g baseball going at 95 mph has a kinetic energy of 130 J. You're crazy.
posted by gijsvs at 12:10 PM on March 11, 2010

Response by poster: you'd need 190 K * 0.020 * 1.5 = 5.7 kJ of heat to raise the surface to ignition temp.

Now, how fast do you need to go at sea level to generate 5.7 kJ of heat in about 60 feet of distance? Assume the ball doesn't ablate or otherwise disintegrate.
posted by Cool Papa Bell at 12:33 PM on March 11, 2010

The first very very half-assed way that occurred to me as a way of computing this: you want to raise the temperature at the surface of the baseball to a few hundred C, which (assuming the gas remains ideal-ish) means a pressure amplification of ~20. The ram pressure on the baseball is proportional to the density of air, times the velocity of the ball squared. Back of the envelope calc says about a km per second, faster than the speed of sound.
posted by chalkbored at 12:43 PM on March 11, 2010

Best answer: This sort of thing is actually a really complicated problem. There are a lot of effects that happen; at the speeds you're looking at, you'll probably see all kinds of nastiness in terms of shocks and other compressibility effects, not to mention all the other heat transfer-related problems.

We can, however, do a really awful first estimate using the stagnation temperature. The stagnation point of a flow is the point where the local velocity is zero, right on the surface of the ball. This point should be right at the front of the baseball, and at that location all of the kinetic energy of the flow is going into heating.

So if we look at the equation given in the link I put above, using a (desired) stagnation temperature of 212 C and an ambient temperature of 22 C, with C_p,air = 1003.5 J/kgK, we get:

V ~ (2*1003.5*(212-22))^(1/2) = 617.5 m/s = ~1380 mph

This is a very bad estimate. It's completely neglecting conduction through the ball, which would drastically lower the temperature -- there would be a big heat loss through the back of that surface. There are blowing effects (particles leaving the surface that carry energy with them), shock heating (radiation being emitted from a shock in front of the ball), reactions in the flow, and all kinds of other nonsense.

To be a little bit more realistic but much less concrete, it would probably be several hundred miles per hour faster than that to even see any kind of ignition, and probably several hundred miles per hour faster than that to see any kind of sustained burning.

It doesn't help that ignition in and of itself is a difficult process to define/understand. The surface of the leather per se isn't what's burning; it's volatile compounds being released by the heating of the leather which combust when they combine with oxygen in the presence of high temperatures.

On preview:

To generate 5.7 KJ of heat, considering that kinetic energy is (1/2)mV^2, we'd need V to be:

V ~ (2*5700/0.02)^(1/2) = ~755 m/s = ~1690 mph

(using gijsvs's calculation of mass and energy -- don't know if these are totally right but they sound okay)

So, close* to what I predicted above using the stagnation temperature. That's assuming that all of the kinetic energy goes into heating up the ball, which would certainly not be the case.

All in all, I'd say you'd have to be going at somewhere between 2000-3000 mph to really make that sucker burn. I'd like to see a catcher that could handle that. There would be a sonic boom (or several) as the ball broke the sound barrier, if it could actually go that fast without completely disintegrating from forces before it caught on fire. I don't even want to calculate the acceleration and forces involved.

*in engineering terms
posted by malthas at 12:48 PM on March 11, 2010 [16 favorites]

I can't think of even a magic device which could accelerate a baseball to a high enough speed to catch fire while preserving the ball as a ball in that small a distance.

The inertialess engine was common in the E.E. 'Doc' Smith fiction series.
posted by nomisxid at 12:48 PM on March 11, 2010

Oh yeah, note: I'm a grad student studying ablation for my master's thesis/research position. So this is essentially what I do. If you want a better calculation, let me know and I'll see what I can do with the computational tools I use.
posted by malthas at 12:50 PM on March 11, 2010

Have Randy Johnson throw it.

After he's doctored it with white phosphorous.
posted by three blind mice at 1:12 PM on March 11, 2010

malthas, if the OP doesn't request it, I will. I'd be pretty interested to hear about how that turned out. Unless it's very time-consuming, of course.
posted by TimeTravelSpeed at 1:22 PM on March 11, 2010

Response by poster: If you want a better calculation, let me know and I'll see what I can do with the computational tools I use.

I think you pretty much nailed it in sufficient terms for me. Thanks!
posted by Cool Papa Bell at 1:43 PM on March 11, 2010

The terminal velocity of a baseball is about 95 miles an hour.

That can't be right.
posted by iknowizbirfmark at 2:24 PM on March 11, 2010

That can't be right.

Sounds about right to me. Terminal velocity for a sky diver is about 140 MPH, and smaller objects have a lower ratio of mass to cross section. Also, a baseball isn't very dense. And a sphere turns out to not be a very good shape aerodynamically speaking.
posted by Chocolate Pickle at 5:05 PM on March 11, 2010

The terminal velocity of a baseball is about 95 miles an hour. That's as fast as a baseball will travel through the Earth's atmosphere near sea level at 1G of acceleration. As it won't burn up under those circumstances, you need a lot more speed.
Terminal velocity is entirely irrelevent here. Terminal velocity only applies to falling, it's the speed at which the drag on the object is equal to the force of gravity. Since we're "throwing" the ball, it doesn't matter.
posted by !Jim at 9:53 PM on March 11, 2010

Terminal velocity is entirely irrelevent here.

I understand. When valkryn first mentioned it, I think that he also understood the relevance. His reference was in the practical context of "But how will it even get going fast enough to actually reach setting on fire speed? Just look, even terminal velocity is only 95 miles per hour."

I was just saying that seemed counterintuitive to me. But the internets seem to think it's that or lower. Learning about only somewhat related concepts is one of the reasons I love questions like this one.
posted by iknowizbirfmark at 1:45 PM on March 16, 2010

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