ON THE EFFECT OF ALTITUDE UPON THE DISTANCE .sx REQUIRED FOR AN AIRCRAFT TO TAKE OFF AND .sx CLIMB 20 METRES , GIVING GENERALISED CURVES OF .sx WEIGHT REDUCTION NECESSARY IF A GIVEN AIR- .sx CRAFT IS TO COMPLY WITH THE REQUIREMENTS OF .sx A.P. 1208 UNDER ADVERSE ATMOSPHERIC CONDITIONS .sx By K. T. Spencer , B.Sc. , A.M.I.C.E. .sx Presented by the Director of Scientific Research , Air Ministry .sx Reports and Memoranda No .sx 1307 .sx ( Ae .sx 447 .sx ) October , 1929 .sx Summary .sx This report presents generalised curves from which a rapid estimate can be made of the amount by which the total weight of an aircraft must be reduced when it has to be flown from an aerodrome under adverse atmospheric conditions , e.g. at height or in the tropics .sx It is assumed that the distance to take off and climb 20 metres under standard ground level conditions has already been determined during the official flight trials for a Certificate of Airworthiness .sx Starting from this figure and from the horse-power loading of the aircraft at the time the official flight trials were carried out , the maximum permissible total weight at which the aircraft may take off under tropical conditions can be obtained from the curves given .sx If in any case the measured value of get-off run at ground level is not available , the curves can be used to give an approximate figure for weight reduction at height if the stalling speed is known .sx The taking-off requirements for civil aircraft are given in Design Leaflet F.1 of A.P.1208 Airworthiness Handbook for Civil Aircraft .sx A maximum horizontal distance is specified in which the aircraft must take-off and clear an obstacle of 20 metres , this distance being 546 yards , 656 yards or 820 yards , according to the category of the aircraft .sx In paragraph 6 of this leaflet it is stated that when it is known that an aircraft is to operate in atmospheric conditions differing considerably from the British conditions it is advisable for the applicant to apply for a Certificate of Airworthiness under the adverse conditions , or alternatively it is for the users of the aircraft to ascertain the reduction in load necessary to enable the normal requirements to be fulfilled .sx The purpose of the present report is to examine the effect of height and weight reduction on the run to take-off , and to put forward a simple and quick method of estimating with sufficient accuracy the necessary reduction in weight when an aircraft has to take-off from an aerodrome under adverse atmospheric conditions .sx It will be convenient to describe first how the proposed method will be used in practice , the theoretical basis on which the curves are constructed being given later .sx It is assumed that the following details of the particular aircraft concerned are known :sx ( i ) The measured distance to take-off and climb 20 metres under standard ground level conditions .sx This is a routine test forming part of the official flight trials carried out prior to the issue of a Certificate of Air-worthiness .sx ( ii ) The total weight of the aircraft at the time the above test was carried out , and the horse power of the engines .sx It is required to determine the maximum permissible total weight of the aircraft when flown from an aerodrome the " equivalent height " of which differs considerably from standard sea level .sx Referring to Fig. 1 , the value of a constant " A " is determined from the ordinate and abscissa corresponding to ( i ) and ( ii ) above .sx Then the ratio can be read off from Figs .sx 2 , 3 or 4 ( depending upon the Category of the aircraft ) , corresponding to the already determined value of " A " and the curve appropriate to the equivalent height of the aerodrome concerned .sx The total horse power is known , and hence the maximum permissible flying weight is determined , .sx The following example will make the method clear :sx Given .sx Under standard ground level conditions the measured run to get off and climb 20 metres is 368 yards , the total weight of the aircraft being 4,700 lb .sx and the horse power 470 .sx Required .sx The necessary reduction in weight if the aircraft is to it take-off and climb 20 metres in not more than 546 yards , from .sx an aerodrome the equivalent height of which is 9,000 ft .sx From Fig. 1 , the value of " A " corresponding to 368 yards and .sx is 1.48. From Fig. 2 with " A " = 1.48 the value of corresponding to 9,000 , ft .sx is 8.7. Hence maximum permissible flying weight is 470 x 8.7 = 4,090 lb .sx and necessary percentage reduction in weight is = 13 per cent .sx Theoretical Basis of the Curves .sx 2 .sx References .sx R. & M. 680 .sx The distance required to take-off an aeroplane , by R. McKinnon Wood and F. B. Bradfield .sx R. & M. 996 .sx On the necessary size of aerodromes in order that a landing may be made if the engine fails when getting off , by H. Glauert .sx R. & M. 1172 .sx The effect of wind , weight and atmospheric conditions ( including semi-tropical conditions ) on the distance to take-off and land an aircraft , by B. H. Rolles and H. L. Stevens .sx The method described below was suggested by Mr. H. Glauert .sx Assumptions .sx The attitude of the aircraft during the run along the ground and during the subsequent climb is assumed to be the same' at height as at sea level .sx The value of under climbing conditions is also assumed to be invariant with height .sx Experience has shown that these assumptions are very approximately true in practice , and in addition any small departures from these conditions will not be important as the rate of change of climb and airscrew efficiency with attitude and is small in this region .sx The following relationships , applicable to that part of the total distance to take-off during which the aircraft is air borne , arise out of these assumptions .sx Since W = ( i ) = constant , since the attitude of the aircraft is constant ( ii ) .sx is constant , hence , so that .sx = constant ( iii ) .sx From the energy equation ( iv ) it follows that ( v ) .sx = constant , by ( iii ) ( v ) .sx In general P varies as nr , so that from ( v ) .sx = constant ( vi ) .sx By ( iii ) ( vii ) .sx From ( vi ) and ( vii ) ( viii ) .sx or Usually r will be in the neighbourhood of 1 .sx Taking this value formula ; .sx Hence the initial assumptions involve a variation of total weight in the same ratio as the decrease in engine power with height .sx Horizontal distance to climb 20 metres .sx ( s2) .sx The equation for climbing flight is or = constant by ( ii ) and ( iii) .sx Hence , since the angle of climb is constant , the horizontal distance required to climb 20 metres will also be constant at all heights if the total weight is varied as .sx Run along ground to attain flying speed .sx ( s1) .sx The equation for the run along the ground is ( see R. & M. 996 .sx ) Compare the conditions at any instant during the run under standard .sx ground level conditions , with those at a corresponding instant during the run at height which has the same value of .sx The following .sx relationship will apply to both points :sx From ( iv ) :sx Assuming as before that , then Hence when r = 1 , = constant , and so by ( xii ) above = constant .sx But is constant for the two points the conditions at which are being compared .sx Hence J is also constant , so that and therefore = constant also .sx From this it follows from ( x ) that = constant .sx by ( ii ) and since , ( xiv ) .sx Effect of altitude and weight variation on s1 + s2 .sx - From the foregoing it appears that if the weight of the aircraft is varied as , the run , L , to get off and climb 20 metres at height is given by where s1 and s2 are the distances under standard ground level conditions for the run to leave the ground and to climb 20 metres respectively .sx Rearranging From this it follows that if the weight is decreased in the same ratio as the total run to get off and climb at height will always be slightly less than the run at ground level , since is less than unity .sx This suggests the following method of attack .sx Starting from the at ground level for the given aircraft , assume the weight to be increased to , m being for the moment unknown , but chosen so that when mW is reduced by the factor pe the run at height is the required standard length L. and can be calculated by the method given in R. & M. 996 corresponding to and the stalling speed .sx Equation ( xv ) above will then relate m and for any given value of L. .sx 7 .sx Construction of the generalised curves .sx The points on Figs .sx 1 .sx and 5 have been calculated as described in R & M. 996 .sx The constant " A " represents , this parameter having been chosen as it is independent of the change in weight m. The calculated points are given in Table I. .sx Figs .sx 2 , 3 and 4 have been calculated from equation ( xv ) in conjunction with Figs .sx 1 and 5 .sx A number of values of and have been taken .sx Fig. 5 gives the corresponding value of .sx For any given height the term .sx of equation ( xv ) can now be calculated , and hence , for a given L , s1 + s2 is fixed .sx Reference to Fig. 1 gives the value of corresponding to this value of and the appropriate " " .sx The ratio of this to the original value of gives in .sx The maximum allowable weight at height so that the run to get off and , climb 20 metres shall not exceed L is therefore .sx As previously described , when using the curves the value of " A " will be determined from Fig. 1 , knowing and .sx This in effect applies an overall correction to the calculated quantities so that the calculations are adjusted to give the correct measured run to take-off and climb at ground level .sx If this measured distance is not available " A " can be calculated from the known horse power loading and stalling speed .sx EXPERIMENTS WITH A SUPERCHARGED .sx SINGLE-CYLINDER UNIT .sx By G. F. MUCKLOW , D.Sc. .sx Communicated by Professor A. H. GIBSON , D.Sc. .sx Reports and Memoranda No .sx 1460 .sx November , 1931 .sx I. Summary .sx - ( a ) Introduction and Object of Experiments .sx - The following paper deals with experiments carried out in the Engineering Laboratory of the University of Manchester on two different types of aero-engine cylinder .sx The cylinders were mounted on a R.A.E. Universal test bed , and supplied with compressed air from a separately driven Reavell compressor , the air being passed through an inter-cooler before being supplied to the carburettor .sx The object of the experiments was to examine the effects of increased induction pressure , at a range of compression ratios , on the behaviour of the cylinders in regard to such variables as power output , heat losses and fuel consumption .sx The cylinders used for the tests were :sx - ( 1 ) A Napier E.77 type , two-valve , all steel cylinder ; and ( 2 ) a Rolls-Royce F. type , four-valve cylinder , having a steel liner and aluminium alloy head .sx ( b ) Range of Investigation .sx - A set of trials was first carried out using the Napier cylinder , at compression ratios of 4.5 to 1 , 4.0 to 1 , and 3.5 to 1 .sx " Straight " Shell No .sx 1 petrol was used , the engine speed being 1,600 r.p.m. throughout .sx At each compression ratio trials were run at a number of super-charge pressures , the complete mixture range being explored as far as possible at each pressure .sx This process was continued until severe detonation rendered a further increase in induction pressure inadvisable .sx During each trial measurements were made of the induction pressure , the power output , the petrol and air consumption , and the heat flow to cylinder jackets and to exhaust .sx With the Napier cylinder , separate trials were run at each compression ratio when the maximum cylinder pressure was recorded at a range of compression ratios , using an Okill pressure indicator .sx On completion of the above tests , the Rolls-Royce cylinder was mounted on the test bed and a second set of trials was carried out at an engine speed of 1,600 r.p.m. .sx