By Chief Engineer JOHN LOWE, U.S. Navy.

The purpose of this article is to point out an easy method whereby any intelligent engineer can determine the point at which it is most economical to cut off the admission of steam into his cylinder.

In the attack upon such a problem, it is useful to employ all the senses which can be brought to bear upon it; for this purpose, diagrams will be used, in order that the sense of sight may assist the brain in forming its conclusions.


Steam Engine Economy


Fig. XABCX is an ideal indicator card, taken from a cylinder, imagined to be 600 feet long, in which the piston, making one stroke per minute, has therefore a piston speed of 600 feet per minute. Divide this card into any convenient number of ordinates, distant dx feet from each other, writing upon each the absolute pressure measured upon it from the zero line XX.

By way of example, let the diameter of the cylinder be 29.59 inches, and let the back pressure from all causes be 7 pounds uniformly throughout. It will be represented by the line b, b, etc. This quantity subtracted from the pressures p, p, etc., leaves the remainder (p-b) upon each ordinate, which remainder represents the net pressures which at that point may be applied to produce external power.

If, now, A is the area of the piston, then the external power (d W) produced between each ordinate is:

To any convenient scale, upon each ordinate, set off the appropriate power as calculated by this equation (1).


dW = --------------. (1.)


There will result the curve w, w, w, determining the power which at any point in the diagram is to be regarded as a gain, to be carried to the credit side of the account.

It is evident that, so long as the gains from expansion exceed the losses from expansion, it is profitable to proceed with expansion, but that expansion should cease at that point at which gains and losses just balance each other.

To Calculate The Losses

The requisite data are furnished by the experiments conducted some years since by President D.M. Greene, of Troy College, for the Bureau of Steam Engineering, U.S. Navy.

According to these experiments, the heat which is lost per hour by radiation through a metallic plate of ordinary thickness, exposed to dry air upon one side and to the source of heat upon the other, for one degree difference in temperature, is as follows:

 Condition. Heat units.

Naked...................................... 2.9330672

Covered with hair felt, 0.25 inch thick.... 1.0540710

" " 0.50 " .... 0.5728647

" " 0.75 " .... 0.4124625

" " 1.00 " .... 0.3070554

" " 1.25 " .... 0.2746387

" " 1.50 " .... 0.2507097

If now t' = temperature of steam at the ordinate,

t = temperature of the surrounding atmosphere,

dS = surface of the cylinder included between each ordinate,

k = that figure from the table satisfying the conditions,

then the power loss (dR) per minute will be:

k (t'-t)dS

dR = ( -- ) ----------. (2)

60 33,000 

To the same scale as the power gains, upon each ordinate, set off the appropriate power loss, as calculated by this equation (2).

There will result the curve r, r, r, which determines the power which at any point in the diagram is to be regarded as a loss, to be carried to the debit side of the account. This curve of losses intersects the curve of gains at a point (it is evident) where each equals the other.

Therefore this is the point at which expansion should cease, and this absolute pressure is the economic terminal pressure, which determines the number of expansions profitable under the given conditions.

In the foregoing example are taken k = 0.3070554, t' = 331.169, t = 60, while the back pressure was taken at 7 pounds.

By way of further illustration, first let the back pressure be changed from 7 to 5.

By equation 1 there will result a new curve of gains, W, W, W, a portion only being plotted.

 Second, let t' = 331.169 as before.

t = 150 instead of 60.

k = 0.2507097 instead of 0.3070554. 

There will result the second curve of losses, R, R, R, intersecting the second curve of gains at the point F, the new economic point for our new conditions.

These two examples fully illustrate the whole subject, furnishing an easy and, when carefully made, a very exact calculation and result.

The following are a few of the general conclusions to be drawn:

1. That radiation is a tangible and measurable cause, sufficient to account for all losses heretofore ascribed to an intangible, immeasurable, and wholly imaginary cause, viz., "internal evaporation and re-evaporation."

2. In order to prevent the high initial temperatures now used becoming a source of loss, it is necessary to prevent the quantity dS (t'-t) becoming great, by making dS as small as possible. In other words, we must compound our engines. Thus for the first time is pointed out the true reason why compound engines are economical heat engines.

3. The foregoing reasoning being correct, it follows that steam jackets are a delusion.

4. In order to attain economy, we must have high initial temperatures, small high pressure cylinders, low back pressures from whatsoever cause, high piston speeds, short rather than long strokes, to avoid the cooling effects of a long piston rod; but especially must we have scrupulous and perfect protection from radiation, especially about the cylinder heads, now oftentimes left bare.