Engineering topics
Publications and source records attributed to Munk, Max M.
In the following note, prepared for the National Advisory Committee for Aeronautics, this induction factor is determined from the result of a model test, and compared with a formula recently developed by the author. The two results are found to be in substantial agreement.
This note has been prepared for the National Advisory Committee for Aeronautics. It deals with the model rules relating to aeronautical problems, and shows how the characteristics of one airplane can be determined from those of another airplane of different weight or size, and of similar type. If certain rules for the ratios of the dimensions, the weights and the horsepower are followed, a small low-powered airplane can be used for obtaining information as to performance, stability, controllability and maneuverability of a larger prototype, and contrariwise.
This note, prepared for the NACA, contains a discussion of the meaning of vortices, so often mentioned in connection with the creation of lift by wings. The action of wings can be more easily understood without the use of vortices.
Dihedral and sweep back can properly be compared only to the extent to which their action is similar in a side slip. In general the rolling moments due to side slip are about three to six times greater for a given dihedral angle than for an equal angle of sweep back.
This report contains a description of a new and useful method suitable for the design of propellers and for the interpretation of tests with propellers. The fictitious slipstream velocity, computed from the absorbed horsepower, is plotted against the relative slip velocity. It is discussed in detail how this velocity is obtained, interpreted, and used. The methods are then illustrated by applying them to model tests and to free flight tests with actual propellers.
This report describes the new method for making computations in connection with the study of rigid airship, which was used in the investigation of the navy's ZR-1 by the special subcommittee of the National Advisory Committee for Aeronautics appointed for this purpose. It presents the general theory of the air forces on airship hulls of the type mentioned, and an attempt has been made to develop the results from the very fundamentals of mechanics without reference to some of the modern highly developed conceptions, which may not yet be thoroughly known to readers uninitiated into modern aerodynamics, and which may, perhaps, for all time remain restricted to a small number of specialists.
This report is a critical study of the results of propeller model tests with the view of obtaining a clear insight into the mechanism of the propeller action and of examining the soundness of the physical explanation generally given. The nominal slip-stream velocity is plotted against the propeller tip velocity, both measured by the velocity of flight as a unit. Within the range corresponding to conditions of flight, the curve thus obtained is a straight line. Its inclination depends chiefly on the effective blade width, its position on the effective pitch. These two quantities can therefore be determined from the result of each propeller test. Both can easily be estimated therefrom for new propellers of similar type. Thus, a simple method for the computation of propellers suggests itself.
In the slipstream behind a propeller there is a considerable amount of kinetic energy which has been imparted to it by the engine without producing any corresponding propeller thrust. The increased absorption of power reduces the propeller efficiency. Attention has been previously directed to this question by Bendemann and Madelung and other writers. Their contribution serves to verify a simple method of calculating the reduction in the propeller efficiency due to the slip stream. That method of calculation is given here. Explanations and examples are given for as single propeller and for two propellers mounted in tandem.
In this paper the application of the slip curve method to the design and analysis of windmills is discussed and illustrated by example.
This analysis was made in the same way as Dr. Durand's tests. Only the thrust is examined.
Wind-driven propellers are much used as sources of power for equipment such as radios. This report establishes the principles involved and acquaints the reader with rules for design of such windmills.
This report discusses the general considerations for the design of aerodynamic laboratories. The dimensions, construction, and components of the wind tunnel are given special attention.
The integration is accomplished by the use of the mean camber of the section at particularly selected points. Simple graphical constructions of the zero directions are derived from the results.
This report contains three new relations extending the modern theory of aeronautics. They deal with phenomena in a frictionless fluid. The first part contains a relation between the power absorbed by an aerofoil and the power absorbed by a propeller. In the second part the exactness of the ordinary formula for the induced drag of an aerofoil is examined and the error is determined. In the third part the author shows that for the calculation of the air forces on bodies of considerable volume the imaginary sources and sinks equivalent to the flow around the body can be used in the same way as vortices are used for the calculation of lift and induced drag of wings.
This report is a discussion of the results of tests with Zeppelin airships, in which the propellers were stopped as quickly as possible while the airship was in full flight. In this paper the author refers to the theory involved in these tests and calls attention to one scientifically interesting fact which can be derived from the tests and which has not yet been noted. The most important question concerning the tests is, of course: does the negative acceleration of an airship with stopped propellers supply proper data for determining the drag of the airship when in uniform flight? This can not be absolutely answered, however, except that in this particular case the agreement is sufficient and that the data obtained from the test are the true quantities, or, at least, the approximate quantities wanted.
This report deals with the calculation of the equilibrium, statistical stability, and damping of the tail plane. The author has simplified the present theory of longitudinal stability for the particular purpose of obtaining one definite coefficient characteristics of the effect of the tail plane. This coefficient is obtained by substituting certain aerodynamic characteristics and some dimensions of the airplane in a comparatively simple mathematical expression. Care has been taken to confine all aerodynamical information necessary for the calculation of the coefficient to the well-known curves representing the qualities of the wing section. This is done by making use of the present results of modern aerodynamics. All formulas and relations necessary for the calculation are contained in the paper. They give in some cases only an approximation of the real values. An example of calculation is added in order to illustrate the application of the method. The coefficient indicates not only whether the effect of the tail plane is great enough, but also whether it is not too great. It appears that the designer has to avoid a certain critical length of the fuselage, which inevitably gives rise to periodical oscillations of the airplane. The discussion also shows the way and in what direction to carry out experimental work.
This report contains a new, simple method of calculating the air forces to which thin wings are subjected at small angles of attack, if their curvature is not too great. Two simple integrals are the result. They contain only the coordinates of the wing section. The first integral gives the angle of attack at which the lift of the wing is zero, the second integral gives the moment experienced by the wing when its angle is zero. The two constants thus obtained are sufficient to determine the lift and moment for any other angle of attack. This with the theory of the aerodynamical induction, and with our empirical knowledge of the drag due to friction, the results are valuable for actual wings also. A particular result obtained is the calculation of the elevator effect. (author)
This report deals with the air forces on biplane cellule. The first part of the report deals with the two-dimensional problem neglecting viscosity. The variation of the section, chord, gap, stagger, and decalage are investigated, a great number of examples are calculated, and all numerical results are given in tables. For the biplane without stagger it is found that the loss of lift in consequence of the mutual influence of the two wing sections is only half as much if the lift is produced by the curvature of the section as it is when the lift is produced by the inclination of the chord to the direction of motion. The second part deals with the influence of the lateral dimensions. It is found that the loss of lift due to induction is almost unchanged, whether the biplane is staggered or not. In the third part conclusions from previous investigations are drawn, viscosity and experimental experience are brought in, and the method is simplified for practical application. Simple formulas give the drag, lift, and moment. In order to make use of the simple formulas more convenient, tables for the dynamical pressure, induced drag, and angle of attack are added so that practically no computation is needed for the application of the results.