This is a pretty interesting video about fungi.

Even though Richard Hammond is pretty cool, he does confuse speed with acceleration. When you say “fastest in the world,” I expect you to talk about the change in position with respect to time. This is different than the acceleration, which is change in velocity with respect to time. Ok, but other than that — nice video.

What about the acceleration of these other objects?

Hammond says that the acceleration of the Pilobolus fungi spores is greater than a bullet, a missile (actually, I think he called a bullet a missile), a jet and a rocket. Let me start with an estimation of the acceleration of these things.

A bullet. Let me look at two bullets: a hand gun and a rifle. The rifle will clearly have a higher speed, but it will take a longer time to get to that speed (I guess). First, for a rifle I will look at the Barrett M95. I know nothing about this gun except that it appears to have a long range. Wikipedia lists it has having a barrel length of 1.143 meters and the bullet has a speed of up to 928 m/s. If the bullet accelerates with a constant acceleration along the length of the barrel, what is the acceleration? First, in one-dimension, I can write the acceleration as:

But I do not know ?t. But I do know v₁ (it starts at rest) and v₂ (the muzzle velocity). I can also write the average velocity during this same time interval as:

Solving this second expression for the time, I can put that into the first expression (and eliminate v₁ since that is equal to 0 m/s):

I know the change in position (the barrel length) and I know the final speed. This gives an average acceleration of 3.8 x 10⁵ m/s². And that is, as Richard Hammond would say, very fast (but really it is a very high acceleration).

What about a hand gun? What gun to choose? What about the Desert Eagle? This has a barrel length of .357 meters (for the longer version) and a muzzle velocity of about 490 m/s. Using the same calculation has above, this gives an average acceleration of 3.2 x 10⁵ m/s².

I am not going to look at a jet or a rocket (or even a missile). There is no way these have accelerations as high as the bullet. First, for the jet, an acceleration of 3 x 10⁵ m/s² would be large enough to kill a pilot. Missiles are fast, but they seem to be on the order of a jet rather than a bullet.

Acceleration of a spore

Since Hammond made a mistake about speed vs. acceleration, I think maybe I shouldn’t trust his acceleration calculations. Luckily, I found a nice article with pictures and videos of accelerating spores.

Yafetto L, Carroll L, Cui Y, Davis DJ, Fischer MWF, et al. 2008 The Fastest Flights in Nature: High-Speed Spore Discharge Mechanisms among Fungi. PLoS ONE 3(9): e3237. doi:10.1371/journal.pone.0003237

Why aren’t all articles as easy to access as this?

First, I can use this image (from the awesome paper) to scale the video.

Where the length of the black bar is 1 mm. Now I can use the video version of the same thing and Tracker Video analysis to get the following plot of horizontal position vs. time. Oh, and this video has a frame rate of 50,000 frames per second.

But what is the acceleration? I guess I could look at this two ways. First, I could try fitting a quadratic equation to the position data to get the acceleration. Or I could look at the velocity data. Here is a plot of the horizontal velocity of the spore.

Since the average acceleration is defined as:

The slope of the velocity-time graph is the average acceleration. You can see the fitting equation gives an average acceleration of 6 x 10⁴ m/s². Impressive – but not as large of an acceleration as I would have thought.

If I only use the first 3 data points, I can get the acceleration up to 1.2 x 10⁵ m/s².

There is one important point – look at the velocity the spore gets to, only around 7 m/s. Both the cited paper above and Richard Hammond say the spores can get to speeds up to 25 m/s. Actually Richard Hammond says that the spores go zero to twenty. Twenty what? I guess either he meant 20 mph (9 m/s) or 20 km/hr (5.5 m/s). But if the spore reached a much higher speed of 25 m/s in about the same amount of time (just a guess) then it could have an acceleration about three times as much, so around 3.6 x 10⁵ m/s².

Back to Hammond. He claims 0 to 20 in 2 x 10^-6 seconds. The acceleration here would depend on the units for the velocity. If I go with 20 m/s then the acceleration would be 1 x 10⁷ m/s². 20 mph would give an acceleration of 4.5 x 10⁶ m/s². And 20 kmh would give an acceleration of 2.7 x 10⁶ m/s².

Hammond also claims that this would be 20,000 g’s. 1 g is 9.8 m/s², so 20k g’s would be 1.9 x 10⁵ m/s². Ok – I have no clue what he did. The 20,000 g’s must be wrong. That is on the same order as the acceleration of a bullet.

What about that PLOS paper? What does it list for the acceleration of the spore? It lists the acceleration of the pilobolus spore at around 2.1 x 10⁵ m/s². Ok, I can buy that. Close to the value that I obtained with video analysis. The paper also lists the acceleration of the Ascobolus immersus spore at 1.8 x 10⁶ m/s² – greater than the pilobolus.

So in the end:

• Does the pilobolus have a large acceleration? Yes.
• Is it the highest in nature? Probably not.
• Is it greater than a bullet? Maybe (but a bullet might not fall under the category “nature”).
• Is it possible I will have another post looking at the motion of a spore? Very likely.