Theory of the flight of Rockets.
THEORY OF THE FLIGHT OF ROCKETS.
A Rocket, being properly constructed, with its rod and other appendages attached, fixed in a vertical position, and fire being applied to its mouth, it will (as experience proves) ascend in the air with a prodigious velocity: but upon inquiry into the cause of this ascent, we meet with difficulties little contemplated when we were viewing the beautiful path it described in the medium of its flight.
That this ascent is dependent on the medium (or air) in which it is generated, admits not of a doubt; but to describe how, or in what manner it is effected, has engaged the attention of some of the most eminent philosophers. In consequence several theories have been advanced for the explication of the phenomena, and among them those of Mariotte and Desaguliers have claimed the most particular attention.
Mariotte attributes the rise of Rockets to the resistance, or reaction of the air against the gas, which is generated by the combustion of the composition.
This hypothesis seems to explain the phenomena; but great objections have been brought against it, on account of the difficulty which attends the reduction of it to mathematical investigations:—this difficulty arises from the law which the propelling force must necessarily observe; that is, it will decrease as the velocity increases, in consequence of the partial vacuum left behind the Rocket in its flight; so that the velocity becomes as it were both a datum and quæsitum; and the correct solution of the problem necessarily involves the integration of partial differences of the highest order.
The hypothesis of Desaguliers is somewhat different to the foregoing; it is much more familiar with mathematical investigations; as it reduces the whole theory to the most simple form; and we think it is not far from being consonant with the known principles of the phenomena; notwithstanding the argument brought against it by Dr. Rees, and his Editors; and which we shall endeavour to prove by citing higher authority than our own.
Dr. Desaguliers illustrates his hypothesis in the following manner:—Conceive the Rocket to have no vent at the choak, and to be set on fire in the conical bore; the consequence would be, either that the Rocket would burst in the weakest place, or that, if all parts were equally strong, and able to sustain the impulse of the flame, the Rocket would burn out immoveable. Now, as the force of the flame is equable, suppose its action downwards, or that upwards, sufficient to lift forty pounds; as these forces are equal, but their directions contrary, they will destroy each other’s action.
Imagine then the Rocket opened at the choak; by this mean the action of the flame downwards is taken away, and there remains a force equal to forty pounds acting upwards, to carry up the Rocket, and the stick or rod it is tied to.
Accordingly we find that if the composition of the Rocket be very weak, so as not to give an impulse greater than the weight of the Rocket and stick, it does not rise at all; or if the composition be slow, so that a small part of it only kindles at first, the Rocket will not rise.
To this we shall add the late Doctor Hutton’s philosophy, on the ascent of Rockets; who says, that at the moment when the powder begins to inflame, its expansion produces a torrent of elastic fluid, which acts in every direction; that is, against the air which escapes from the cartridge, and against the upper part of the Rocket; but the resistance of the air is more considerable than the weight of the Rocket, on account of the extreme rapidity with which the elastic fluid issues through the neck of the Rocket to throw itself downwards, and therefore the Rocket ascends by the excess of one of these forces over the other.
This, however, would not be the case, unless the Rocket was pierced to a certain depth. A sufficient quantity of elastic fluid would not be produced; for the composition would inflame only in circular coats, of a diameter equal to that of the Rocket; and experience shows that this is not sufficient. Recourse then is had to the very ingenious idea of piercing the Rocket in a conical hole, which makes the composition burn in conical strata, which have much greater surface, and produce a much greater quantity of inflamed matter and fluid. This expedient was certainly not the work of a moment.
The stick serves to keep it perpendicular; for if the Rocket should begin to tumble, moving round a point in the choak, as being the common centre of gravity of Rocket and stick, there would be so much friction against the air by the stick, between the centre and the point, and the point would beat against the air with so much velocity, that the reaction of the medium would restore it to its perpendicularity. When the composition is burnt out, and the impulse upwards has ceased, the common centre of gravity is brought lower towards the middle of the stick, by which means the velocity of the point of the stick is decreased, and that at the point of the Rocket is increased; so that the whole will fall down, with the Rocket end foremost.
During the time the Rocket burns, the common centre of gravity is shifting and getting downwards, and still faster and lower as the stick is lighter; so that it sometimes begins to tumble before it is quite burnt out: but when the stick is too heavy, the common centre of gravity will not get so low, but that of the Rocket will rise straight, though not so fast.
From the experiments of Mr. Robins, and other Gentlemen, it was found that the Rockets of two, three, or four inches diameter, rise the highest; and they are found to rise to all heights in the air, from 400 to 1,254 yards, which is about three-quarters of a mile. For further particulars respecting the theory of the flight of Rockets our readers are referred to Robins’s Tracts, vol. 2.—Philosophical Transactions, vol. 46, page 578: and more particularly to Mr. W. Moor’s “Treatise on the motion of Rockets,” in which they will find the subject elegantly treated.
[SECTION VII.]
TABLES OF VARIOUS COMPOSITIONS.
1. Serpents.—Mealed-powder one pound, salt-petre one ounce and three-quarters, charcoal one ounce.
2. Pin Wheels.—Mealed-powder twelve ounces, salt-petre three ounces, sulphur one ounce and a-half, steel-filings two ounces.
3. Common Stars.—Salt-petre one pound, sulphur four and a-half ounces, antimony four ounces, isinglass half an ounce, camphor half an ounce, spirits of wine three-quarters of an ounce.
4. White Stars.—Mealed-powder four ounces, salt-petre twelve ounces, sulphur six ounces and a-half, oil of spike two ounces, camphor five ounces.
5. Blue Stars.—Mealed-powder eight ounces, salt-petre four ounces, sulphur two and a-half ounces, isinglass two ounces, spirits of wine two ounces.
6. Tailed Stars.—Mealed-powder three ounces, salt-petre one ounce, sulphur three ounces, charcoal one ounce.
7. Drove Stars.—Salt-petre one pound, sulphur eight ounces, antimony four ounces.
8. Pointed Stars.—Salt-petre eight and a-half ounces, sulphur two ounces, antimony one ounce and three-quarters.
9. Stars of a fine colour.—Mealed-powder one ounce, salt-petre one ounce, sulphur one ounce, oil of turpentine four drams, camphor four drams.
10. Variegated Stars.—Mealed-powder eight drams, roch-petre four ounces, vivum two ounces, camphor two ounces.
11. Brilliant Stars.—Mealed-powder three-quarters of an ounce, salt-petre three ounces and a-half, sulphur one and a-half ounce, spirits of wine one ounce and a quarter.
12. Tailed Stars.—Salt-petre four ounces, sulphur six ounces, antimony two ounces, rosin four ounces.
13. Ditto with Sparks.—Mealed-powder one ounce, salt-petre one ounce, camphor two ounces.
14. Gerbes.
1. Mealed-powder one pound and a-half, coarse iron-sand five ounces.
2. Mealed-powder two pounds, coarse iron-sand eight ounces, salt-petre one pound.
15. Roman Candles.—Mealed-powder half-a pound, salt-petre two pounds and a-half, sulphur half-a pound, glass-dust half-a pound.
16. Tourbillons.
For four ounce cases.—Mealed-powder one pound two ounces, charcoal two ounces and a-quarter.
For eight ounce cases.—Mealed-powder two pounds, charcoal four ounces three-quarters.
17. Showers of Fire.
Chinese.—Mealed-powder one pound, sulphur two ounces, iron-sand first order five ounces.
Ancient.—Mealed-powder one pound, charcoal two ounces.
Brilliant.—Mealed-powder one pound, iron-sand first order four ounces.
18. Golden Rain.
1. Mealed-powder four ounces, salt-petre one pound, sulphur four ounces, brass-dust one ounce, saw-dust two ounces and a-quarter, glass-dust six drams.
2. Mealed-powder twelve ounces, salt-petre two ounces, charcoal four ounces.
3. Salt-petre eight ounces, sulphur two ounces, brass-dust a quarter of an ounce, antimony three-quarters of an ounce, saw-dust twelve drams, glass-dust one ounce.
19. Silver Rain.
1. Mealed-powder two ounces, salt-petre four ounces, sulphur two ounces, antimony two ounces, sal-prunella half an ounce.
2. Salt-petre half an ounce, sulphur two ounces, charcoal four ounces.
3. Mealed-powder two ounces, salt-petre four ounces, sulphur one ounce, steel-dust three-quarters of an ounce.
20. Water Rockets.
1. Mealed-powder three pounds, salt-petre two pounds, sulphur one pound and a-half, charcoal two pounds and a-half.
2. Salt-petre one pound, sulphur four pounds and a-half, charcoal six pounds.
3. Salt-petre one pound, sulphur four ounces, charcoal twelve ounces.
4. Mealed-powder four ounces, salt-petre one pound, sulphur eight ounces and a-half, charcoal two ounces.
21. Sinking Charge for Ditto.
Mealed-powder ten ounces, charcoal one ounce.
22. Water Serpents.
1. Mealed-powder one pound, charcoal one pound.
2. Mealed-powder one pound, charcoal nine ounces.
23. Water Balloons.
1. Mealed-powder two pounds, salt-petre four pounds, sulphur two pounds, antimony four ounces, saw-dust four ounces, glass-dust one ounce and a-quarter.
2. Mealed-powder three pounds, salt-petre four pounds and a-half, sulphur one pound and a-half, antimony four ounces.
24. Wheel Cases.
1. Mealed-powder two pounds, salt-petre four ounces, steel-filings six ounces.
2. Mealed-powder two pounds, salt-petre twelve ounces, steel-filings three ounces.
3. Mealed-powder four pounds, salt-petre one pound, sulphur eight ounces, charcoal four ounces and a-half.
4. Mealed-powder eight ounces, salt-petre four ounces, saw-dust one ounce and a-half, charcoal one ounce.
5. Mealed-powder twelve ounces, saw-dust half an ounce, charcoal one ounce.
6. Salt-petre one pound nine ounces, sulphur four ounces, charcoal four ounces and a-half.
25. Slow Fire for Wheels.
1. Mealed-powder one ounce and a-half, sulphur two ounces, salt-petre four ounces.
2. Antimony one ounce six drams, sulphur one ounce, salt-petre four ounces.
26. A Dead Fire for Wheels.
Salt-petre one ounce and a-half, sulphur a quarter of an ounce, antimony two drams, lapis calaminaris a quarter of an ounce.
27. For Standing or Fixed Cases.
1. Mealed-powder two pounds, salt-petre one pound, sulphur half-a-pound, charcoal half-a-pound.
2. Mealed-powder one pound, salt-petre half-a-pound, steel-dust four ounces.
3. Mealed-powder ten ounces, charcoal two ounces.
4. Mealed-powder half-a-pound, sulphur two ounces.
5. Mealed-powder one pound and-a-half, saw-dust three-quarters of an ounce, charcoal two ounces and a-half.
28. For Sun Cases.
1. Mealed-powder two pounds two ounces, salt-petre five ounces, sulphur one ounce, steel-dust twelve ounces.
2. Mealed-powder one pound and a-half, salt-petre three ounces, steel-dust three ounces and three-quarters.
29. For Spiral Wheels.
Mealed-powder fourteen ounces, salt-petre one pound and a-half, sulphur six ounces, glass-dust fourteen ounces.
30. Globes.
Salt-petre six ounces, sulphur two pounds, camphor two ounces, antimony four ounces.
31. Serpents for Pots des Brins.
Mealed-powder ten ounces, salt-petre six ounces, charcoal one ounce and a-half.
32. Fires of Different Colours.
White Fire.—Gunpowder two parts, steel filings one part; for a pale white add a little camphor. Raspings of ivory give a flame of a silver colour, somewhat dazzling to the eyes.
Red Fire.—Gunpowder two parts, iron-sand of the first order one part. Greek pitch produces a flame somewhat red, but more inclined to a bronze colour.
Common black pitch produces a dusky flame, like a thick smoke, very essential in producing a medium of intolerable obscurity.
Sulphur, mixed in a moderate quantity, makes the flame appear of a blue cast.
Sal ammoniac and verdigris produce a flame inclined to green.
Raspings of yellow amber give to the flame a lemon colour.
Crude antimony a kind of russet colour.
33. For Jets of Fire.
When the inner diameter of the cases is not more than six lines the following must be the proportions.
Chinese Fire.—Mealed-powder one pound, salt-petre one pound, sulphur eight ounces, charcoal two ounces.
White Fire.—Iron-sand of the first order eight ounces, mealed-powder eight ounces, salt-petre one pound, sulphur three ounces, charcoal three ounces.
But when their calibre is from eight to twelve lines, the following are the proportions.
White Fire.—Mealed-powder one pound, salt-petre one pound, sulphur eight ounces, charcoal two ounces.
Chinese Fire.—Salt-petre one pound four ounces, sulphur five ounces, charcoal five ounces, iron-sand of the third order twelve ounces.
Brilliant Fire.—Mealed-powder one pound, iron-sand five ounces.
For Jets of Larger Dimensions.
Chinese Fire.—Salt-petre one pound four ounces, sulphur seven ounces, charcoal five ounces, and twelve ounces of a compound of the six different kinds of sand.
34. Sparkling Compositions for Choaked Cases.
For Black.—Mealed-powder and charcoal.
For White.—Salt-petre, sulphur, and charcoal.
For Grey.—Mealed-powder, salt-petre, sulphur, and charcoal.
For Red.—Mealed-powder, charcoal, and saw-dust.
These may be used in any proportion the practitioner may think proper, for a little experience will prove to him that various colours of fire may be produced by only varying the proportions or order of the ingredients, or by rendering them alternately predominant. The same observation will apply to many other cases of a similar nature.
[SECTION VIII.]
Compound Fire-Works.
Compound Fire-Works are those resulting from the combination of the single or more simple kind; principally those which we have already described. The number and variety of figures, and the modification of which they are susceptible, is almost endless, and to describe all, or the greater part of them, would far exceed the limits of our Manual. We shall therefore consider it sufficient to select such specimens of simple arrangement as will form a proper introduction to those which are more complex; in which latter case the young Pyrotechnist must be left to his own ingenuity, which will readily dictate to him a greater variety than it would be possible for us to describe.