Rockets by Robert Goddard

Author:Robert Goddard [Goddard, Robert]
Language: eng
Format: epub
ISBN: 9780486174341
Publisher: Dover Publications
Published: 2012-10-15T04:00:00+00:00

(9)

and t is at once obtained from the relation

(10)

whence, of course, a is at once known.

The calculation of and call for no comment; and R is obtained as P, the mean ordinate between v0 and v1 from the curves as already explained, multiplied by S and .

The value of M, the initial mass, for the interval, necessary in order that the final mass in the interval shall be one pound, is then obtained from equation (7); and finally. the ratio of equations (6) to (7) (i. e.,) is calculated. This is the ratio of the initial mass necessary, including losses due to both R and g, to the mass necessary to give the one pound the same velocity, v1, without overcoming R and g; and the entire calculation must be repeated until a minimum value of this ratio is obtained—when the corresponding.. mass, M, will be the minimum mass for the interval in question. Each minimum M is marked in the tables by an asterisk.

This process is carried out for each interval beginning with the first.

It should be noticed that, although P and the density are not really constant in any interval, the result obtained by taking the mean of the quantities must nevertheless give results close to the truth, owing to the fact that P increases during the ascent, whereas the density decreases.

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