Abstract :
The paper falls logically into three divisions: (1) A general review of the principal laws of the dissipation of heat, — radiation, conduction and convection. (2) the development of a simple formula for the effect of altitude on the cooling of surfaces of different shapes, and (3) a general discussion of the method of conducting experimental observations at different altitudes, on three different shaped surfaces. 1. The first division is principally historical in that the most reliable data is given as found from former laboratory investigations, to determine (a) the laws of heat dissipation and (b) the effects of various factors on these laws. This is given as a preparatory step to determining the formula in division 2. 2. It is shown in the second division that, where the loss by convection varies as the 1.25 power of the temperature rise and as the 0.5 power of pressure, the “temperature rise” varies as the 0.4 power of pressure. It is then shown that the temperature rise increases, in going from a lower to a higher altitude, at a uniform rate of about 5 per cent for each 1000 meters change in elevation. Since this applies only to loss of heat by convection, a correction factor is added to reduce this effect when radiation (same in vacuo as in gas) enters into the dissipation of heat. This factor is first expressed in percentage of convection loss to total loss, and then expressed in terms of the developed surface effective for convection, and the envelope surface effective for radiation. This is called the “shape-factor” S. The percentage increase in temperature then is equal to 5 AS where A is the difference in altitude expressed in kilometers. The above is for a loss unaffected by temperature. Where the loss is in copper windings, an increase in temperature, due to changes in pressure, has the effect of increasing the loss, which in turn still further increases the temperature rise. It is shown by mathematical treatment- that this effect increases the value 5 AS to 5.85 AS for all copper loss. For various ratios of copper to iron loss (unaffected by temperature), the term becomes, close enough for practical purposes, AS (5 + α), where a is percentage of copper loss to total loss. The calculated values are then compared with the observed values. 3. In this division the method of carrying on the experimental observations is gone into somewhat in detail.
