determinations, a sure and certain test is the amount of ballast taken,
together with the volume of gas in the balloon at starting, and the
space left for expansion, supposing that the ascent is made with only a
partial inflation.
It is useless to boast of distance or height, unless sand equal to the
occasion can be taken in the car; and if the diameter and depth of the
machine is not in conformity with well established rules, no confidence
should be placed in unsupported vapourings, as all the accessories to
which I refer must be in order and bear comparison, one with another.
In a voyage this year by German officers from Berlin, the exact number
of bags of ballast they took up led me to guess the capacity of the
balloon, allowing for the number of passengers, and the supposed weight
of the whole; I found that I was pretty near the mark, and that the
expenditure of sand was about in proportion to my own when I took Mr.
Walter Powell a journey of 250 miles.
The balloon itself is no bad indicator of what can be achieved,
especially in vertical motion, that is by showing the extent of
expansion when the silk is throughout fully distended, and if it be
so, by the force with which the gas rushes out of the safety valve; it
in this way helps and checks barometrical readings, and may at times
approximately take the place of that instrument for a rough-and-ready
intimation of the height. For example, if a balloon mounts up when only
half full at starting, and afterwards rises so high that gas escapes
from the neck, then it must be between three and four miles high,
roughly speaking.
It is of no use for a novice or an unscientific aëronaut to tell a
fanciful tale about his lofty flights to fabulous elevations, when he
is known to have taken only a moderate amount of ballast, and only one
person besides himself in the car.
If one hears a story that a small aërial affair has been up miles high,
or hundreds of miles horizontally, even at a low altitude, do not take
it for granted that you have been told the truth, you can easily try
and prove it for yourself. Just ask a few questions as to its size,
next get at its displacement of air, as you would judge in like manner
of a ship’s displacement of water when it has to carry so many thousand
tons of cargo.
If you hear that a balloon of thirty or even forty feet in diameter has
been 20,000 feet high when filled with coal gas, shake your head and
fly to figures, remembering that the following simple calculations will
enable you to judge for yourself. Make, in fact, yourself a balloon of
tissue or Chinese paper, and bear in mind at the outset the proportion
that the _diameter_ bears to the circumference of a circle.
Say you make it of three feet diameter, or thirty-six inches.
In order to find the circumference, which is three times and
one-seventh the diameter, multiply the diameter thirty-six by 3·1416--
Then 3·1416
36 inches.
------
188496
94248
--------
113·0976
========
_Secondly._--By multiplying this circumference 113, by the diameter
36, it gives the superficial surface.
113
36
----
678
339
----
Number of superficial inches on the surface 4068
====
This multiplied by one-sixth gives the contents in cubic inches--
4068
6
------
24408
======
Then if 24408, the contents of a balloon three feet in diameter is
divided by 1728, the number of cubic inches in a foot, you have
fourteen cubic feet as the capacity of a three feet balloon, thus--
1728) 24408 (14 cubic feet
1728
----
7128 and
6912
----
216 inches over.
====
If you want to find the internal capacity of a balloon three feet in
diameter, first multiply the three feet by three feet to give the
circumference (nine feet), which gives twenty-seven, the surface.
Then multiply by 5236 to ascertain the cubic contents.
5236
27
------
36652
10472
--------
14·1372 being 14 cubic feet and a fraction.
========
14
I will just give one more simple calculation of the capacity and
superficial surface of a balloon thirty-three--instead of three--feet
in diameter.
33
33
----
99
99
----
1089 circumference.
33 diameter.
------
35937 surface.
·5236 decimal numbers.
------
215622
107811
71874
179685
----------
18816·6132 cubic contents.
==========
Carburetted hydrogen or coal gas, should raise from 402 pounds, as
1,000 feet of light gas should raise 40 pounds to the 1,000 cubic feet.
If the reader is desirous of calculating either for model balloons,
or, as to the size, capacity, and power of larger balloons, take note
of this concise and abridged table of the diameters, surfaces, and
capacities, together with the ascensive power for every foot capacity
for hydrogen, so that if coal gas is used, allowance must be made
accordingly.
First, for miniature paper or skin balloons.
Feet, Diameter. Surface Capacities Pounds
in Square. in Cubic Feet. Ascensive Power.
1 3-1/10 0-1/2 0-2/32
3 28 14 1 {in nearly
{a pound.
6 113 113 7
10 314 523 33
20 1,257 4,189 261
LARGER BALLOONS.
30 2,827 14,137 884
40 5,026 33,510 2,094
50 7,854 65,450 4,091
80 20,106 268,083 16,755
100 31,416 523,599 32,725
The striking advantage of enlarging balloons, arises from the fact,
that their powers increase faster than their surfaces. When the
diameter is doubled, four times as much material is required, but you
get eight times as much capacity.
I have now offered a few plain calculations in order to assist those
who feel interested in the subject, they may be extended and more
scientifically pursued in another volume of my experiences, when they
will be required, perhaps, for illustration of other ascents.
I am often asked, how high will a balloon go? Will it mount higher and
higher until gas is let off to stop it?
My answer is, that when a balloon, after inflation, is brought to
an even balance, in other words, when so much ballast is placed in
the car, that it shows a very slight tendency to move upwards, then
the required ascending power is increased by putting out more sand,
say to the amount of twenty, thirty, or forty pounds, according
to circumstances, I mean the strength of wind at the time, and the
proximity of adjacent objects, such as trees and buildings.
With either of these limited number of weights removed, the balloon
cannot rise very high, unless there is either a large space for
expansion, or a very much larger quantity of sand is put out
subsequently.
I will simply try this position by asking the reader to suppose that
A and B, two rival aëronauts, are about to engage at one and the same
time with two balloons of similar capacities to reach an elevation, say
of six miles, and that both balloonists have balloons that will contain
each 100,000 cubic feet of coal gas, and that they each take up one
person, so that the weight of their respective balloons, each having to
raise two persons, will altogether be 1,000 pounds for A’s and the same
for B’s machine.
A’s balloon is to be quite filled with gas that lifts forty pounds the
1,000 feet, but B’s balloon is to be only half filled.
On testing the lifting power, A’s being full, that is containing
100,000 cubic feet of gas, will, after deducting the weight of balloon
and two persons calculated at 1,000 pounds, with 3,000 pounds weight of
ballast.
But B’s balloon would only have a 1,000 pounds of sand as compared with
A’s, because B’s is only half full, having only 50,000 feet of gas in
it.
Well, under these apparently opposite conditions, which balloon, do you
suppose, would attain the greatest height?
I should say, paradoxical as it may appear, that they would reach
about the same height, because the space left for expansion in B’s
balloon, owing to its half filled state, would admit of the gas
doubling its volume, while A’s balloon, being filled at starting,
would from the first irrecoverably lose gas from the neck, although it
remained full to the safety valve.
B’s would hold its own 50,000 feet, and it would quickly increase and
multiply up to 100,000 cubic feet, and thus equal A’s balloon.
The store of ballast would soon be equal. A’s 3,000 pounds would, at
three and three quarter miles high, be reduced to the level of B’s,
which was 1,000 pounds at starting, with only 50,000 cubic feet of gas.
I have frequently adopted this system, but as I shall advert in the
next part of my experiences to cases in point, I prefer now to refer
to two of Mr. Green’s high ascents in proof of the practicability and
objects of this method, which saves labour in casting out so much sand,
and saves expense as well.
The two voyages of Green, which were made in the years 1838-9, have
altogether escaped notice in the recent reviews of the most remarkable
scientific ascents in the present century.
Robertson’s, Gay-Lussac’s, Bixio’s, and Barral’s having been mentioned,
but not those of Green, which came after the ascents of above
experimenters, and long before the fatal one by Croce Spinelli and
Sivel, and that lately made by Captain Jovis and Lieutenant Mallet.
On the 4th of September, 1838, the celebrated Nassau balloon, which at
that time was the property of Messrs. Gye & Hughes, the proprietors
of Vauxhall Gardens, ascended from them with Mr. Green, Mr. Edward
Spencer, and Mr. Rush of Elsenham Hall, Essex, the latter gentleman
having engaged the balloon for experimental purposes, and more
particularly on this occasion for ascertaining the greatest altitude
that could with safety be attained with three persons in the car; and
further to ascertain the changes of temperature that would take place
at different elevations, as well as the variations of the currents
of air; and finally, to establish the important fact, as to whether
the same difficulties with regard to respiration in a very rarified
atmosphere would be experienced by persons rising in a balloon to any
great altitude, as have been felt by persons who have ascended lofty
mountains, and by previous aërial travellers in balloons to great
heights.
They left the earth at twenty-five minutes before 7 p.m. with two
barometers standing at thirty inches each.
One of these instruments, as well as a thermometer, was furnished
by Mr. Rush, constructed on the most accurate principles, and made
expressly for the purpose.
The thermometer stood at 66° Fahrenheit.
The following were the variations:--
Barometer. Thermometer.
30 inches. 66 degrees.
23 ” 56 ”
21 ” 53 ”
19 ” 46 ”
18 ” 42 ”
17 ” 39 ”
16 ” 35 ”
15 ” 25 ”
Greatest altitude 14·70 ” 25 ”
On first rising they took a north-westerly direction; at 2,500 it
changed to the north, and shortly afterwards to north-east.
Their journey was pursued towards Epping, and they were discharging
ballast all the time. Leaving Dunmow to their left they attained their
greatest altitude, namely, 19,335 feet, or three and a half miles and
855 feet.
In consequence of the great quantity of sand discharged after clearing
the Metropolis their ascent became very rapid, and, from the great
expansion of the inflating power, the gas rushed out from the lower
valve in considerable torrents.
The velocity of their upward progress caused the balloon to rotate in a
spiral motion with astonishing rapidity.
During their trip about 1,200 pounds of ballast was discharged, but
they reserved 100 pounds by which to regulate the descent.
During their descent, when at 1,200 feet from the earth, a heavy
fall of snow was encountered, accompanied by a sudden and very great
reduction of temperature, the thermometer dropping to 22°, or 10° below
freezing point. The mercury in the barometer at this moment had risen
to nineteen inches.
I mention this circumstance for the purpose of showing that sometimes
sudden changes of temperature have been experienced, not only by Green,
but by Bixio and Barral later on in the present century.
The fatigue of the muscular powers, occasioned by exertion in emptying
ballast, did not occasion any serious inconvenience in respect to
difficulty in respiration.
We shall see, in the next ascent which was still higher, that the
plan I have already exemplified as to allowing considerable space for
expansion was resorted to, and this saved both the necessity for and
the depression consequent upon hard work, although a large volume of
gas was literally wasted, which might, in an economical point of view,
have been prevented; but it will serve to show that a large balloon
partially inflated, with a reduced amount of sand, is for all practical
and scientific purposes preferable to a fully inflated balloon, that
is, for very high ascents.
The ordinary way of examining the specific gravity of the different
gases is by a simple method founded on the principles of pneumatics,
for discovering the relative specific gravities of the aëriform fluids.
This consists in observing the time that a given portion of the gas,
under a determined pressure, takes to escape through a very small
aperture. The density of the gaseous fluid must be inversely as the
square of the interval that elapses.
The weight of the balloon and all appendages must evidently compress
the included gas, and thereby render it in some degree denser.
To compute this minute effect, we have only to consider that the
pressure of a column of atmosphere at the mean temperature, and near
the level of the sea, is 1632 pounds on a circle of a foot in diameter.
Thus, in a balloon of sixty feet in diameter, if we suppose the whole
load to have been 6000 pounds, the compression of the bag would only
amount to five-thirds of a pound for each circle of a foot in diameter
in the horizontal action, or corresponding to the 979th part of the
entire pressure of the atmosphere.
But the weight of the confined gas (hydrogen) being 1200 pounds, its
buoyancy must have suffered a diminution of somewhat more than a pound
or one-eleventh from the circumference opposed to it.
But as I have purposely abstained from giving in this first elementary
part any computations of an abstruse order by more learned and capable
writers than myself, I shall reserve further remarks on this particular
head for my subsequent volume.
ASCENT, OVER FIVE MILES HIGH, BY GREEN AND RUSH.
I have before me a mass of leading articles and newspaper cuttings
alluding to the ascent of Messrs. Jovis and Mallet, in which honourable
mention is made of the lofty explorations by Robertson and L’Hoest,
Gay-Lussac, Bixio, and Barral, together with Mr. Glaisher’s and my
own, but Green’s with Rush are invariably omitted, and yet these were
quite as important, while the second was higher than that made by the
intrepid French balloonists, and, so far as physical results go, the
Englishmen do not appear to have fainted or been much troubled.
It is of immense importance to note this, as there can be no doubt
that a certain zone exists, in entering which some persons are more
susceptible than others to lessened atmospheric pressure, and here they
begin to feel the bad effects, which, by the way may come on without
warning, just as it is with Alpine travellers, although there are
marked distinctions between the two, but we cannot enter upon that in
detail in this chapter.
This trip, by Green, was one of those which was designed to add a
fraction of knowledge to the already existing stores of science. This
fact is sufficient, even according to those who are not great admirers
of ballooning, to warrant its encouragement when taken in hand by
those who do not affect to be mere aëronautic performers, embarking
in aërostatic pursuits for sensational objects, or with the vain and
delusive idea, that it is not dangerous, and that it is a money-making
concern.
Mr. Rush, assisted by the knowledge of his coadjutor, threw a character
of deep interest over the whole subject of aërostation, and this
trip, though lost sight of, at the present moment, is well worthy of
re-production, serving as it does, two ends; firstly, to call attention
to the fact, that English aëronauts seem to get more toughened by
acclimatization to rarified air than Frenchmen, and secondly, that they
do such work with less ado, and with equal, perhaps a little more,
methodical foresight and precision, than our more dashing and mercurial
neighbours.
It was on the 10th of September (what a number of exceptionable
journeys were made in this month!) that the highest ascent which had
been made up to that date, came off from the far-famed Vauxhall Gardens.
The proprietors made arrangements with Mr. Rush for it to take place
in the afternoon, that gentleman engaging the car for the occasion.
The time allowed for preparation was limited. The first object to be
gained was that of diminishing the weight of the apparatus to as low a
point as due regard to their personal safety would admit.
A small car was substituted for that commonly used. At five o’clock
in the afternoon, Green ascertained the power of the gas with which
the “Nassau” balloon was charged, the tranquil state of the weather
rendered this an easy operation.
On examination, Green found that the whole weight of the balloon and
its appendages was 4,084 pounds thus constituted:
Balloon, netting and car 700 pounds.
Ballast 1,500 ”
Mr. Rush 145 ”
Mr. Green 145 ”
Light, grapnel and rope 52 ”
Cloaks and barometers, &c. 30 ”
Twenty-seven half-hundredweights
slung round the hoop 1,512 ”
------
Total 4,084 ”
======
Please to note that Green then opened the upper valve, and
discharged a quantity of gas equal to the power of the twenty-seven
half-hundredweights, which were then removed from the hoop.
Why, you will ask, was this gas wasted, or put into the balloon? I
suppose for the sake of appearances and symmetrical distention, but
had Rush not been paymaster, it would most assuredly never have entered.
The departure took place with an ascending power of 112 pounds--very
considerable indeed.
Barometer stood at 30·50 just before leaving, and thermometer at 60°;
before seven minutes had elapsed, they had fallen, the former to 20,
and the latter to 36°, equal to 11,000 feet or two miles.
Had it not been for the miserable aspect the balloon would have
presented, more gas would have been let off equal to an additional
1,000 pounds, and then not more than 500 pounds of sand need have been
shipped.
At 11,000 feet they were driven south, after going north-east.
Green was continually casting out ballast; on attaining 16,000
feet--three miles--they entered a current blowing at the estimated
speed of sixty miles an hour, though they never stated, more’s the
pity, how under such a rocket-like rush upwards, they found time to
determine that this wonderful current existed.
The only inconvenience (this is noteworthy) Mr. Rush sustained, arose
from the constant escape of gas from the rapid ascent.
Mr. Green suffered severely from the cold in his hands and feet.
They were now exposed to the influence of roaring winds, but from what
I can make out, it was only the effect of quick vertical ascent; here
the aëronaut, owing to the exertion he had to undergo, found it a
matter of the utmost difficulty to fetch his breath.
The greatest altitude reached was 27,146 feet, indicating an elevation
from the earth of 5 miles and 746 feet, the barometer, at this point
having fallen from 30·50 to 11, and the thermometer from 61° to 5° or
27° below the freezing point.
Ballast had been reduced to something under seventy pounds, which Green
resolved on preserving, and the result of their descent, which was
never minutely entered into, proved the propriety of this reservation.
In the descent, they discovered something which very much bore the
appearance and consistency of snow. Mr. Rush’s attention was called
to it, but after consideration they were inclined to think that the
substance was not snow, but the dew and moisture congealed by the cold.
It would be instructive to know how Captain Jovis, who must have had
the night dew on his balloon at the early inflation in Paris, got on
in this respect. His idea was that the sun would dry the moisture,
but I was under the impression that there would scarcely be time for
a globular shaped machine to get dry all round during the inflation.
However, they may, like Green, have encountered a snow storm without
there being, as indeed was unlikely, any damp clouds overhead at that
elevation; what I mean is, if the balloon itself shed and shook off
innumerable particles of frozen moisture, there can be no wonder that
such was noticed and mistaken for a fall of snow.
After Rush and Green had hovered over Lewes in Sussex, a descent was
effected near Southover; there was not much hovering _I should say_.
In this ascent they had the double advantage of witnessing the setting
sun (prior to their quitting the earth) and on their reaching 12,500
feet of being once more within the sun’s rays.
Another important consideration bearing upon this chapter is the
celerity with which balloons make their ascent.
It is obvious that the efficient power of ascension, or the excess of
the whole buoyant force above the absolute weight of the apparatus,
would, by acting constantly, produce always an accelerated motion. But
this is very soon checked, and a uniform progress maintained by the
increasing resistance which the huge mass must encounter in its passage
through the air.
The velocity which a balloon would gain from unobstructed acceleration
must, from the theory of dynamics, be to that which a falling body
acquires in the same time as the efficient buoyancy is to the aggregate
weight of the apparatus and of the contained fluid. Thus, if a balloon
were to rise with a force equal to the eighth part of its compound
weight, the celerity resulting from a constant acceleration would be
expressed by multiplying four feet into the number of seconds elapsed
since it was launched into the air. Its advance, however, being
opposed, the balloon though still affected with partial oscillations,
the final velocity is effected in perhaps little more than double the
time required without such obstruction.
This final velocity, or the velocity at which the ascent becomes
uniform, the resistance from the air being then equal to the efficient
buoyancy of the balloon, is easily calculated.
The resistance a circle encounters in moving through any fluid in the
direction perpendicular to its plane, is measured by the weight of a
column of that fluid, having the circle for its base, and an altitude
equal to the height from which a heavy body in falling would acquire
the given celerity.
Near the level of the sea, and at the mean temperature, a column of
atmospheric air seventeen feet high, and incumbent on a circle of one
foot in diameter, weighs a pound avoirdupois, which is, therefore, the
resistance that a circle would suffer if carried forwards with the
celerity of thirty-three feet each second.
According to the same theory, however, which we owe to the sagacity
of Newton, the resistance of a sphere is just the half of that of
its generating circle, and consequently a velocity of forty-six and
two-fifths feet in a second through the air would in ordinary cases
create a resistance of one pound to a ball of one foot in diameter.
In other circumstances, the quantity of resistance must be proportional
to the square of velocities, and of the diameters. Whence, if the
buoyant power were always the same, the velocity of the ascent of a
balloon would be inversely as its diameter.
I introduce these few observations, which are by a much higher
authority than my own, because it occurred to me that my own remarks
might be considered too homely for some of those who may read these
lines, but as I have merely aimed at affording amusement with a
moderate portion of instruction, and do not write for scientific men,
but for general readers, I shall hope to gradually progress in this
treatment in a subsequent volume.
A JUMP OUT OF THE CAR IN AMERICA.
Among the numerous newspaper reports which are on my table, are several
relative to what, in plain unvarnished English, we should describe as
a parachute descent. But the one I allude to was not like Cocking’s,
Garnerin’s, Le Turr’s, or Hampton’s, it had a size and peculiarity
worth notice.