Speed of a Sperm Cell

The speed of a sperm cell is never constant and is affected mostly by its physiology and environment. A sperm cell always travels through a liquid medium whether it is within the male or female reproductive systems. It has only one mode of transportation -- its flagellum, which is powered by a mitochondrion. The length of the flagellum is one of the factors that determine the swimming speed of the sperm cell.

Also, due to a sperm cell's tiny size (25 μm) and the fluid-filled environment, the viscosity of the sperm cell's surroundings produces the greatest effect on its swimming speed rather than inertial forces that larger organisms would encounter. The Reynolds number of an organism determines how easily viscous drag affects the organism's motion. This number is equal to the inertial force acting on the object divided by the viscous force acting on it. Cells generally experience a Reynolds number of less than 1.

A sperm cell uses its flagellum, commonly referred to as a "tail", to propel itself toward the female oocyte, or "egg". The flagellum is the longest part of the 25 μm of the cell and surprisingly requires only 2 × 10⁻¹⁸ watts of power to propel it. The hydrolysis of a single ATP molecules produces 10⁻¹⁹ joules of energy so cellular motion requires very little energy expenditure.

So why would anyone want to know what the swimming speed of sperm is? If scientists knew the exact or, at least, the approximate value, it could possibly lead to new breakthroughs in contraceptive technology. If the sperm could chemically be slowed down to a point where it is immobilized and is unable to sustain life functions, the "morning after"pill could become the "right after intercourse"pill. The speed of the sperm would be necessary to know the amount of the chemical inhibitors necessary to immobilize it. Immobilizing it could also provide scientists with a deeper understanding of the chemical signals exchanged on the surface of the egg when the sperm arrives.

Eugene Kogan -- 2000

This topic reminded me of the Laurie Anderson song "Mach 20" from her 1984 magnum opus United States Live. Actually the word "song"doesn't adequately describe this track. Anderson is usually considered a performance artist rather than a musician. "Mach 20" consists of a short spoken segment run through a voice processor with a unique electronic instrument playing a vamp in the background. The text of the track is a humorous fusion of biology and information science.

Ladies and Gentlemen. What you are observing here are magnified examples, or facsimiles, of human sperm.

Generation after generation of these tiny creatures have sacrificed themselves in their persistent, often futile attempt to transport the basic male genetic code. But where's this information coming from? The have no eyes. No ears. Yet some of them already know that they will be bald. Some of them know that they will have small crooked teeth. Over half of them will end up as women. Four hundred million living creatures, all knowing precisely the same thing. Carbon copies of each other in a Kamikaze race against the clock.

Now some of you may be surprised to learn that if a sperm were the size of a salmon it would be swimming its seven inch journey at five hundred miles per hour. If a sperm were the size of a whale, however, it would be traveling at fifteen thousand miles per hour or Mach twenty.

Now imagine, if you will, four hundred million blind and desperate sperm whales departing from the Pacific Coast of North America, swimming at fifteen thousand miles per hour, and arriving in Japanese coastal waters in just under forty five minutes. How would they be received? Would they realize that they were carrying information? A message? Would there be room for so many millions? Would they know that they had been sent for a purpose? [mp3]

How accurate is Anderson's scaling from sperm to salmon to whale? To answer this question, we first need to identify a typical length for each entity. These values are from one source each, have not been verified, and are certainly open to debate.

• A typical sperm cell has a 5 μm head on a 50 μm tail for an overall body length of 55 μm*.
• Chinook salmon were chosen as the representative Pacific salmon. Typical adult chinooks range from 20 to 35 inches in length, which averages to about 70 cm**.
• A typical sperm whale is about 19 m* long.

The speed of the salmon and whale quoted in "Mach 20" were divided by the body lengths cited above to obtain the speed in body lengths per second. The results were 320 body lengths per second for the salmon and 353 for the whale.

Given the uncertainty and subjectivity in the length values, the first order equality of these numbers is sufficient to validate the equivalence of the scaled speeds of the salmon and whale to each other. That is to say, if a salmon traveling at 500 mph were scaled up to the size of a sperm whale, it would be traveling at something around Mach 20.

Now, assume a speed for a sperm cell of 336 body lengths per second; that is, the average of the salmon and whale speeds. Multiplying this number by the length of a sperm yields 18,500 μm/s or 18.5 mm/s. This is two or three orders of magnitude (100 to 1000 times) faster than the numbers cited in the student essay above. Sperm swimming at this speed would cover their " seven inch journey" to the ovum (180 mm) in under ten seconds!

The results of this analysis are summarized in the table below.

How fast do sperm swim in terms of body lengths? Given the numbers collected by the student in the essay before this, a reasonable speed would seem to be on the order of 35 μm/s or a little less than two thirds of a body length per second. Scaled up, this corresponds to 45 cm/s (1.0 mph) for the salmon and 12 m/s (27 mph) for the whale.

The results of this corrected analysis are summarized in the table below.

When scaled up, the salmon would be moving as fast as an invalid recovering from surgery and the whale would be moving as fast as a car on a residential street. Since a salmon in the water can easily outpace a human on land and I've seen footage of whales swimming alongside moderately fast boats, these numbers are a definite let down. No one would ever bother to tell you them, let alone write a song about them.

I realize that these are just ballpark figures and it may be that there's a significant error in one or more of them. Still, it seems highly unlikely that any new numbers would to conspire to produce speeds anywhere near those claimed in "Mach 20". This raises two questions.

First, where did Laurie Anderson get the numbers that later became "Mach 20"? I had always considered her an educated artist, but there's no reason to believe she's any more educated in the sciences or more likely to check her facts than anybody else. Is there anyone among us who can claim never to have indulged in scientific gossip? There's even a word for such a thing. It's called a "factoid". In much the same way that science fiction humanoids resemble humans, factoids resemble facts. Factoids are the science done by "They". You know, "They say that cell phones cause cancer" and other such unsubstatiated rumors. If "Language is a Virus" (the name of another track on United States Live) then "Mach 20" is surely proof of this. Who infected Laurie Anderson with the "Mach 20" virus?

Second, what is the fastest creature when speeds are measured in body lengths per second? Is there maybe even some general relationship between size and speed? This is a topic for further research.

Editor's Supplement -- 2000