FIRST STEPS TOWARD SPACE - Smithsonian Institution Libraries

0 it 20 SO 40 90 60 10 BO 90 lot 110 Of 130 140 15V
FIGURE 1.—Correlation of time and acceleration.
tween propulsion force and initial weight of the
rocket.
The time T corresponding to the end of combustion
is given by
,= v (l MA
The rocket velocity Vt at the end of combustion
is given by
„ r M0 i/. MtY
Vt—v \n— — ( 1 — -r-jT-]
f Mt n\ M0/_
The altitude h reached at the end of combustion
is given by
ht= "go
[MJ. Mt , \ . 1 1 /, Mt\
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SMITHSONIAN ANNALS OF FLIGHT
The initial velocity V necessary to climb by force
of inertia from height h to height H, the latter
reached with zero velocity speed is given by
V* = 2g0r (_} LA
\h + r H+r H+r)'
where r is the radius of the earth considered as
spherical.
From the above formula we can obtain the value
of ratio M0 necessary for reaching a previously
established altitude H with zero resulting velocity.
The rocket reaches this altitude by coasting from
altitude h where, at the end of the combustion, it
had velocity V. For this calculation a graph has
been prepared, shown in Figure 2, for a prompt
solution of the problems regarding the rocket's
vertical ascension without taking into account the
resistance of the air.
Regarding the resistance of the air, not considered
until now, and expressed by the above formula (8),
this can be expressed in function of ratio M0jm
where m is the value of the mass at any given time.
In Figure 3 are shown a diagram of function
F(V)'d of the resistance of the air; a diagram of the
relative retarding acceleration WA; and a diagram,
with a linear variation, of the rocket's acceleration
in the absence of air.
NOTES
1. Aldo Bartocci, "Le Escursioni in altezza col motore a
reazione," L'Aerotecnica, vol. 13, no. 12 (December 1933),
pp. 1646-66; and "II Razzo," L'Aerotecnica, vol. 14, no. 3
(March 1934), pp. 255-66.
2. In a letter to the author, dated 5 July 1949, General
G. A. Crocco said:
I have indeed been pleased that Professor Eula has informed
me that you are the author of the interesting articles published
in 1933, 34, and 38; and I was very glad to have this
confirmation authenticated in writing. .
I am glad then to tell you that the rate of retardation (drag)
introduced by the air in the vertical movement of the rocket,
and which today is published by an English Review, the subject
of which is the rocket "Neptune" of the U.S. Navy,
coincides exactly with that which you designated certainly
for the first time, in 1934.
The article to which he refers may have been that by C. H.
Smith, M. W. Rosen, and J. M. Bridger, "Super Altitude
Research Rocket Revealed by Navy," Aviation, June 1947,
pp. 40-43.—Ed.
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