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pressure of 100 atmospheres. The full lines indi cate the ranges over which calculations were made while over the ranges shown by dotted lines the values were extrapolated. Yours faithfully, in the later articles, however, the specific impulses EVOLUTION OF ENERGY IN shown in the tables are not achieved, due to the J. HUMPHRIES, B.SCENG.(HONS.) facts that in practice finite expansion ratios arc JET AND ROCKET 17 Pinehurst Cottages, used, and also that at temperatures over about Farnborough, Hants. 2000 deg. K. dissociation occurs. In FIG. 1 curves PROPULSION are given showing the variation of specific impulse with mixture ratio for a hypothetical hydro To the Editor, SIMPLIFIED STATICS carbon, CH and oxygen, for both the maxi 1·82 DEAR SIR, mum theoretical values and for a chamber pres DEAR SIR, I should like to add one or two points sure of 100 atmospheres and an expansion ratio With reference to the article by R. Hadekel in to the series of articles by Mr. Bielkowicz of 100:1 including the effects of dissociation. The the August issue of AIRCRAFT ENGINEERING, we entitled "Evolution of Energy in Jet and Rocket results for dissociation in both FIGS. 1 and 2 are should like to add another method of solving the Propulsion". With reference to Tables I and III taken from a report published by Ritter von Stein same problem, viz. determination of jack loads (March) mention is not made of the importance at Trauen in 1942. It will be seen that the specific during retraction, as applied to the main under of the mixture density in choosing a rocket fuel. impulse is down to about 68 per cent of the carriage on the Portsmouth Aviation" Aerocar". Although specific impulse is a major factor most maximum theoretical, and occurs at a slightly An extension of the method using the principle rockets arc designed for high speed flight involv lower mixture ratio. In general with the expansion of virtual work is arrived at by using a velocity ing large losses due to drag, and, as the fuel of a ratios in use today the calculated specific impulse diagram. The method is simple, and involves the rocket is usually a large percentage of the total is about 60-70 per cent of the maximum theoreti minimum of arithmetical calculation. mass, it is important to use a fuel mixture with as cal, while in practice only 90-95 per cent of this high a density as possible. A convenient method of A velocity diagram is drawn by the method latter value is obtained due to combustion and determining the relative merits of various fuel defined below: nozzle losses. In the same figure the variation of mixtures is by means of the "density impulse". Start with a vector cl, of unit length and normal flame temperature is shown, allowing for dis This is a figure obtained by multiplying the speci to CL to represent the velocity of L relative to C. sociation. Point b on the velocity diagram is then fixed such fic impulse by the relative density of 'the fuel that the position of b relative to cl is similar to mixture, this giving a measure of the impulse TABLE I—IN ALL CASES THE OXIDIZER IS OXYGEN that of B relative to CL. Now ab is drawn normal per unit volume. In Tables I and II are given the Spec. Fuel Density to AB and cd is drawn normal to CD. These two specific impulses, densities and density impulses Fuel Imp. mixture impulse I density Id for the fuels examined in the first article (Tables lines meet at a point which represents both a and I and III). d on the velocity diagram, since there is no Hydrogen 530 0·440 233 456 0·800 365 relative motion between A and D. This point also It will be seen from Table I that on the basis of Heptane 455 0·991 451 is called j since J has no velocity. f and e are Aviation petrol 455 1·002 456 density impulse the mixture liquid hydrogen/ 456 0·997 454 drawn relative to cd and ab respectively. gf and liquid oxygen shows up very poorly against the 453 1·027 465 eg are drawn normal to GF and EG respectively. other fuels listed, and considering the difficulty of 501 0·941 471 ethylene 470 0·923· 437 This fixes point g. It is then put in relative to eg. handling liquid hydrogen the combination does 456 1·052 480 Now jh represents the motion of the point h Ethyl alcohol (complete com not appear to have very great practical possibili bustion) 426 1·010 430 relative to j . This can be split into two components ties. In Table II some of the metal combinations Ethyl alcohol (incomplete com jh parallel to HJ, representing the velocity of 374 0·978 366 seem to open up an interesting field for experi bustion) Glycerine 389 1-186 461 closure of the jack, and jj, representing the ment, although in the only experiments known to Nitro-glycerine . 396 1·6 633 velocity of H normal to HJ. me, conducted by Sanger with a sol of aluminium In the above table all substances which are gaseous at normal powder in Diesel oil with oxygen, no noticeable The point S is the C.G. of the undercarriage. temperature and pressure arc assumed to be in the liquid phase increase in specific impulse was obtained over the at their boiling points. On the velocity diagram the point s is drawn so TABLE II Diesel oil/oxygen combination. As pointed out Spec. Fuel Density that Then, as is the velocity of S relative Reaction Imp. mixture Impulse Fuel I density Id to the fixed points and the vertical component s, a, is the vertical velocity of S. If we assume that Carbon .. 431 1·270 547 C+O →CO 2 2 Carbon .. C+½O →CO 288 1·367 394 the velocity of all components remains constant Phosphorus 2P+2½O →P O 479 1·843 882 1 1 2 over a small increment of time t, then the vertical Silicon .. Si+O →SiO 525 1·482 778 2 2 Silicon .. Si+2F →SiF 504 1·290 650 distance travelled by S in that time is s,a,xt and 2 4 Magnesium Mg+½O →MgO 562 1·431 804 the jack closes a distance j , h x δt. If the under Aluminium 2A1 + l½O →A1 O 566 1·633 924 2 2 2 carriage weight is W, and the jack load is P, then Calcium Ca+F →CaF 566 1·300 736 2 2 Sodium 2Na+½O → 373 1·006 375 2 Na2 O the work done in raising the undercarriage is Sodium Na+½F →NaF 534 1·029 549 s, a, x δt x W and the work done by the jack is Potassium 2K+½O →K O 373 0·897 335 2 2 Potassium K+F →KF 450 0·930 418 j , h x δt x P. Equating these we have: Cadmium Cd+½O →CdO 210 4·707 988 s, a, x δt x W=j, h x δt x P. Iron 2Fe+1½O →Fe O 300 2·823 847 2 1 2 Manganese 3Mn+2O →Mn O 363 2·901 1.052 2 1 4 With reference to the section on the dissocia tion of mixtures of gases FIG. 2 shows the partial This method can be readily extended to take pressures of the products of combustion plotted into account the weights of all the members by against temperature, for the stoichiometric finding their C.G. velocities and including the mixture of the combination CH /oxygen, at a work done on each member in the work equation 1·82 above. Yours faithfully, ELECTRO-HYDRAULICS (MESSIER) LTD. R. G. HOARE, Chief Stressman 336 Aircraft Engineering
Aircraft Engineering and Aerospace Technology – Emerald Publishing
Published: Oct 1, 1946
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