J.B.S. Haldane, On Being the Right Size

JBS Haldane was an Indian geneticist and evolutionary biologist, and a fervent populariser of science. Yes, Indian, because he died an Indian citizen and a professor at the Indian Statistical Institute at Calcutta. I was in fact quite surprised to learn about Haldane’s Indian connection myself; I am told a friend of my father’s had the opportunity to work for Haldane. He was born a British citizen and was a professor at Cambridge and at the University College London before he left Britain for India over objections to Britain’s international policies. He saw in India “the closest approximation to the free world”, which should give those of us who think badly of this country some pause:

Perhaps one is freer to be a scoundrel in India than elsewhere. So one was in the U.S.A in the days of people like Jay Gould, when (in my opinion) there was more internal freedom in the U.S.A than there is today. The “disgusting subservience” of the others has its limits. The people of Calcutta riot, upset trams, and refuse to obey police regulations, in a manner which would have delighted Jefferson. I don’t think their activities are very efficient, but that is not the question at issue.

He was also a card-carrying Marxist, but had his reservations about whether communism would work in the real world. Which brings me to the essay from the title of this post. I was pointed to it by Prof. Mahendra Verma. The essay(text here) came up because we were talking about camber and lift and powered flight. Haldane’s essay is a joy to read, and his keen interest in, and insight into, various branches of science (the social sciences included) beyond biology is evident.

All too often, people tend to ignore the limitations that physics imposes on life. Haldane talks about the limitations that the ability of flight imposes on the animal possessing it. There is, for example, a simple physical reason that objects that fly cannot be too large: the power required to fly grows faster than the size of the object (assuming the shape of the body doesn’t change). Therefore, for instance, “An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts.”

I do have an interesting (to me) technical point to make about the section of the essay that’s about flight. In the essay, Haldane says:

It is an elementary principle of aeronautics that the minimum speed needed to keep an aeroplane of a given shape in the air varies as the square root of its length. If its linear dimensions are increased four times, it must fly twice as fast.

The amount of lift (or drag) that a body can produce in a flow is a function of the Reynolds number (a non-dimensional parameter that combines the velocity of flight, the size of the body, and the resistance from the medium). The square-of-velocity rule that Haldane implicitly assumes is only valid for large Reynolds numbers. For a bird with a wingspan of about 1 metre, flying at about 1 metre per second in air, the Reynolds number is about 100,000. This falls in the regime in which the velocity-squared rule can indeed be applied.

The drag on a sphere as a function of the Reynolds number is still a problem of active interest. At low Reynolds numbers, the drag is proportional to velocity (if you know about the Stokes drag (= 6πμrv), you know this). But the drag increases more quickly than the velocity, becoming proportional to the square of the velocity for large Reynolds numbers (which is to say large velocities, if you assume that the same body as before is being used).

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