Paradoxes of ideality, Part 3
(continued from Part 1 and Part 2)

Y. B. Karasik,
Thoughts Guiding Systems Corp.,
Ottawa, Canada.

Increasing the ideality of one machine is accompanied by decreasing the ideality of another machine

Increase of efficiency (e.g. thermal efficiency, fuel efficiency, electrical efficiency, etc.) of machines requires more efficient cooling systems so that to reduce heat losses. That is why the cooling system becomes more complex, and, hence, less ideal.

For example, the first electrical machines had no cooling system other than natural cooling due to the temperature difference between the machine and the surrounding. Then electrical machines with air cooling appeared. Then electrical machines with water cooling appeared. Then machines that were cooled by liquefied gases appeared, etc. [1]

It looks like evolution of one machine towards the ideal one is accompanied by evolution of another machine towards the anti-ideal one.

Contradictory criteria of ideality

Single-shaft gas turbine engines consumes 30% less fuel as compared to two-shaft gas turbine engines. But the latter are 3 times as lighter than the former ones, occupy less space, cheaper and more reliable [2]. So what are more ideal ? From the standpoint of fuel efficiency single-shaft engines are more ideal. But from the standpoint of other specific characteristics, such as power/volume, power/manufacturing cost, and power/maintenance cost, two-shaft engines are more ideal.

Who are more ideal flyers, birds or planes ?

Birds and planes occupy different niches amongst flyers. Planes fly higher, faster, and farther (without a landing), and carry a much higher payload. Does it mean that they are better (or more ideal) flyers ? How at all compare the efficiency of their flights ?

Both planes and birds lose weight when flying. Planes lose it because burn fuel. Birds lose it because convert fat and carbohydrate energy in their bodies into energy to drive the wing muscles, i.e. into mechanical energy. But birds lose much less proportion of their weight than planes over the same period of time [3]. Birds are more energy efficient flyers.

Let W(t) be the weight of a flyer at an instant t. Let ΔW(t) be the amount of weight loss over the time interval Δt beginning at an instant t. Then


is much less for birds than for planes. Hence,


and, accordingly,

-W '(t)/W(t)    (1)

is also much less for birds than for planes. Expression (1) is the measure of ideality of converting body mass (fuel or fat, etc.) of flyers into their kinetic energy. The same holds for walking/running animals. From the standpoint of this measure, species are much more energy efficient moving bodies than machines.

The measure (1) is valid under the assumption that the rate of fuel/fat consumption does not vary over time. If it does, then the energy efficiency of the flight is given by the formula:

(W(Tstart) - W(Tfinish))/(W(Tstart) × (Tfinish - Tstart))    (2)

It is true for any moving animals or machines, not birds and planes only.

R E F E R E N C E S:

  1. "Technological systems: the laws of evolution", by A. F. Kamenev, "Machine Building" ("Mashinostroyeniye") publishing house, Leningrad, 1985, p. 36.
  2. "Heavy dump trucks' design evolution", by Z. L. Sirotkin, "Machine Building" ("Mashinostroyeniye") publishing house, Moscow, 1971, p. 47.
  3. "Bird Flight - Scientific Analysis of the Efficiency", by C. Johnson, published in the internet in November 2007 (