Airplanes, airships, aircraft engines

Foreword

This book has been prepared with the idea in view of furnishing a good practical knowledge of aircraft to the Naval Service. The nomenclature contained herein was compiled by the National Advisory Committee on Aeronautics, which is without question the best authority on the subject in this country. The writer is indebted to the above committee for the courtesy extended him in authorizing its publication in this book. The writer is also indebted to Lieutenant J. W. Iseman, U.S.N.R.F., and Ensign J. C. Eames, U.S.N. R.F., for valuable assistance rendered in preparation of data on instruments and aircraft engines.

Lieutenant Albert Tucker, (CC), U.S.N.

NOTE

General Order No. 57, dated July 2, 1921, signed by the Secretary of the Navy, states that "Report No. 91 of the National Advisory Committee, entitled 'Nomenclature for Aeronautics' has been adopted as the official nomenclature for Aeronautics for use of the Army and Navy Air Services."

This nomenclature is contained in this book.

A. TUCKER.

Table Of Contents

CHAPTER PAGES

I. Nomenclature for aeronautics, alphabetically.. 11-52 II. Explanations and definitions of various other

terms used in connection with aircraft, etc. . 53-59

Contents

XXV. The recording barograph, description, troubles,

corrections, etc 197-200

XXVI. The tachometer, or revolution counter, description, troubles, corrections, etc 201-205

CHAPTER I Nomenclature for Aeronautics Alphabetically

Aerodynamic pitch. — (See Pitch.)

Aerofoil. — A winglike structure; flat or curved, designed to obtain reaction upon its surfaces from the air through which it moves.

Aerofoil section. — A section of an aerofoil made by a plane parallel to the plane of symmetry of the aerofoil and to the normal direction of motion.

Aeronaut. — The pilot of an aerostat.

Aerostat. — An aircraft which embodies a container filled with a gas lighter than air and which is sustained by the buoyancy of this gas; e.g., airship, balloon.

Aerostatics. — The science which relates to the buoyancy and behavior of light er-than-air craft.

Aerostation. — The operation of balloons and airships. Corresponds to aviation, but refers to lighter-than-air craft.

Aileron. — A hinged or pivoted movable auxiliary surface of an airplane, usually part of the trailing edge of a wing, the primary function of which is to impress a rolling moment on the airplane. (Fig. 1.)

Air scoop. — A projecting cowl, which, by using the dynamic pressure of the relative wind or slip-stream, serves to maintain air pressure in the interior of the ballonet of an aerostat. (Fig. 2.)

Aircraft. — Any form of craft designed for the navigation of the an* — airplanes, airships, balloons, helicopters, kites, kite balloons, ornithopters, gliders, etc.

Airdome. — A field providing facilities for aircraft to land and take off and equipped with hangars, shops, and a supply depot for the storage, maintenance, and repair of aircraft. 11

Aileron-

FIG. t.

Tail j5ocw

FlS.3

Airplane. — A form of aircraft heavier than air which obtains support by the dynamic reaction of the air against the wings and which is driven through the air by a screw propeller. This term is commonly used in a more restricted sense to refer to airplanes fitted with landinggear suited to operation from the land. If the landing gear is suited to operation from the water, the term seaplane ' ' is used . (See defi ni tion . ) Pusher. — A term commonly applied to a single engine airplane with the propeller in the rear of the main supporting surfaces. (Fig. 3.) Tandem. — An airplane with two or more sets of wings of substantially the same area (not including the tail unit) placed one in front of the other and on about the same level.

Tractor. — A term commonly applied to a single engined airplane with the propeller forward of the main supporting surfaces. (Fig. 4.) Airship. — A form of aerostat provided with a propelling system and with means of controlling the direction of movement.

Nonrigid. — An airship whose form is maintained by the

pressure of the contained gas.

Rigid. — An airship whose form is maintained by a rigid

structure contained within the envelope. Semirigid. — An airship whose form is maintained by means of a rigid or jointed keel and by gas pressure. Air speed. — (See Speed.) Air-speed indicator. — (See Indicator.) Altimeter. — An aneroid barometer, mounted on an aircraft,

whose dial is marked in feet, yards, or meters. Anemometer. — Any instrument for measuring the velocity

or force of the wind.

Angle, critical. — The angle of attack at which the flow about f&ACTOZ NOrfOPLAt<£.

FIG. 4 fyppe^cftx an aerofoil changes abruptly, with corresponding abrupt changes in the lift and drag coefficients. An aerofoil may have two or more critical angles, one of which almost always corresponds to the angle of maximum lift.

Angle, dihedral. — The main supporting surfaces of an airplane are said to have a dihedral angle when both right and left wings are upwardly or downwardly inclined to a horizontal transverse line. The angle is measured by the inclination of each wing to the horizontal. If the inclination is upward, the angle is said to be positive; if downward, negative. The several main supporting surfaces of an airplane may have different amounts of dihedral. (Fig. 5.)

Angle, downwash. — The acute angle through which the air stream relative to the airplane is deflected by an aerofoil. It is measured in a plane parallel to the plane of symmetry.

Angle, gliding. — The acute angle which the flight path makes with the horizontal when descending in still air under the influence of gravity alone; i.e., without power from the engine.

Angle, landing. — The angle of attack of the main supporting surfaces of an airplane at the instant of touching the ground in a three point landing; i.e., the angle between the wing chord and the horizontal when the machine is resting on the ground in its normal position.

Angle of attack. — The acute angle between the direction of the relative wind and the chord of an aerofoil; i.e., the angle between the chord of an aerofoil and its motion relative to the air. (This definition may be extended to any body having an axis.)

Angle of incidence (in directions for rigging). — In the process of rigging an airplane some arbitrary definite line in the airplane is kept horizontal; the angle of incidence of a wing, or of any aerofoil, is the angle between its chord and this horizontal line, which may be the line of the upper longerons of the fuselage or nacelle or the thrust line.

Angle of pitch. — The angle between two planes denned as follows: One plane includes the lateral axis of the aircraft and the direction of the relative wind; the other plane includes the lateral axis and the longitudinal axis. (In normal flight the angle of pitch is, then, the angle between the longitudinal axis and the direction of the relative wind.) This angle is positive when the nose of the aircraft rises.

Angle of propeller blade setting. — The angle which the chord of a propeller section makes with a plane perpendicular to the axis of the propeller. This angle varies along the blade, increasing as the boss is approached.

Angle of roll, or angle of bank. — The angle through which an aircraft must be rotated about its longitudinal axis in order to bring its lateral axis into a horizontal plane.

Angle of tail setting. — The acute angle between the chord of the wings of an airplane and the chord of the tail plane.

Angle of yaw. — The angle between the direction of the relative wind and the plane of symmetry of an aircraft. This angle is positive when the aircraft turns to the right.

Angle of zero lift. — (See Zero lift angle.)

Antidrag wires. — (See Wires.)

Antilift wires. — (See Wires.)

Apparent pressure. — The excess of pressure inside the envelope of an aerostat over the atmospheric pressure. In the case of an airship, the excess of pressure is measured at the bottom of the envelope unless otherwise specified.

Appendix. — The tube at the bottom of a balloon, used for inflation. In the case of a spherical balloon it also serves to increase the "head" of gas, and so to build up an internal pressure sufficient to keep the envelope from being pulled out of shape by the weight of the basket. (Fig. 6.)

Aspect ratio. — The ratio of span to mean chord of an aerofoil.

Aspect ratio of propeller. — The ratio of propeller diameter to maximum blade width.

Attack, angle of. — (See Angle.)

Attitude. — The attitude of an aircraft is determined by the inclination of its axes to a "frame of reference" fixed to the earth, i.e., the attitude depends entirely on the position of the aircraft as seen by an observer on the ground.

Automatic valve.— An automatic escape and safety valve for the purpose of regulating internal pressure in an aerostat.

Aviator. — The operator or pilot of heavier-than-air craft. This term is applied regardless of the sex of the operator.

Axes of an aircraft. — Three fixed lines of reference; usually centroidal and mutually rectangular. (Fig. 7.)

The principal longitudinal axis in the plane of symmetiy, usually parallel to the axis of the propeller, is called the longitudinal axis; the axis perpendicular to this in the plane of symmetry is called the normal axis; and the third axis, perpendicular to the other two, is called the lateral axis. In mathematical discussions the first of these axes, drawn from front to rear, is called the X axis; the second, drawn upward, the Z axis; and the third, running from right to left, the Y axis.

Balanced surface. — (See Surface.)

Ballonet. — A small balloon within the interior of a balloon or airship for the purpose of controlling the ascent or descent and for maintaining pressure on the outer envelope so as to prevent deformation.

Balloon. — A form of aerostat deriving its support in the air from the buoyancy of the air displaced by an envelope, the form of which is maintained by the pressure of a contained gas lighter than air, and having no power plant or means of controlling the direction of flight in the horizontal plane.

Barrage. — A small captive balloon, raised as a protection against attacks by airplanes.

Captive. — A balloon restrained from free flight by means of a cable attaching it to the earth.

Kite. — An elongated form of captive balloon, fitted with tail appendages to keep it headed into the wind, and usually deriving increased lift due to its axis being inclined to the wind. A Caquot balloon is of this type. (Fig. 8.)

Nurse. — A small balloon made of heavy fabric, employed as a portable means for storing gas. Sometimes one is so connected as to automatically allow for the expansion or contraction of the gas in an aerostat when on the ground.

Pilot. — A small balloon sent up to show the direction of the wind by observations of its flight with theodolites.

Sounding. — A small balloon sent aloft without passengers but with registering meteorological and other instruments.

Balloon bed. — A mooring place on the ground for a captive

balloon.

Balloon fabric. — (See Fabric.)

Bank. — To incline an airplane laterally. Right bank is to incline the airplane with the right wing down. Also used as a noun to describe the position of an airplane when its lateral axis is inclined to the horizontal. Bank, angle of. — (See Angle of roll.)

Barograph. — An instrument used to make a permanent record of variations in barometric pressure. In aeronautics the charts on which the records are made some-

A*es of an, A/rop/or*e, FIG. 7- times indicate altitudes directly instead of barometric pressure.

Barrage balloon. — (See Balloon.) .

Barrel roll. — An aerial maneuver in which a complete revolution about the longitudinal axis is made, the direction of flight being approximately maintained.

Basket. — The car suspended beneath a balloon for passengers, ballast, etc.

Bay. — The cubic section of a truss included between two transversely adjacent sets of struts of an airplane. The first bay is the one closest to the plane of symmetry.

Biplane. — A form of airplane whose main supporting surface is divided into two parts, superimposed.

Blade back. — The markedly convex surface of a propeller blade which corresponds to the upper surface of an aerofoil.

Blade face. — The surface of a propeller blade, flat or slightly cambered near the tips, which corresponds to the lower surface of an aerofoil.

Blade setting, angle of. — (See Angle.)

Blade width ratio. — The ratio of the width of a propeller blade at any point to the circumference of the circle along which that point travels when the propeller is rotating and the airplane is held stationary. When used without qualifying terms, it refers to the ratio of the maximum blade width to the circumference of the circle swept by the propeller.

Boat seaplane. — (See Seaplane.)

Bonnet. — The appliance, having the form of a parasol, which protects the valve of a spherical balloon against rain.

Boss. — The central portion of an airscrew. The portion in which the hub is mounted.

Bow stiffeners. — Rigid members attached to the bow of a nonrigid or semirigid envelope to reinforce it against the pressure caused by the motion of the airship. (Sometimes called nose stiff eners.)

Bridle. — A sling of cordage which has its ends attached to the envelope of a balloon or airship and a rope or cable running from an intermediate point.

Bulkhead. — A transverse structural member of a fuselage or nacelle, continuous around the periphery.

Buoyancy. — The upward force exerted on a lighter-than-air craft due to the air which it displaces. Center of. — The center of volume of the gas container or the center of gravity of the gas (envelope) of a balloon or airship.

Gross. — The total upward force on an aerostat at rest; the total volume multiplied by the difference of density of the air and the contained gas.

Positive and negative. — The positive or negative difference between the buoyancy and the weight of a balloon or airship. The unbalanced force which causes ascent or descent.

Cabane. — A pyramidal or prismoidal framework to which wire or cable stays are secured.

Camber. — The convexity or rise of the curve of an aerofoil from its chord, usually expressed as the ratio of the maximum departure of the curve from the chord to the length of the chord. "Top camber" refers to the top surface of an aerofoil and "bottom camber" to the bottom surface; "mean camber" to the mean of these two.

Camber ratio. — The ratio of the maximum ordinate of a propeller section is its chord.

Capacity. — The cubic contents or volume of an aerostat.

Captive balloon. — (See Balloon.)

Caquot balloon. — (See Balloon, kite.)

Car. — The nacelle of an airship.

22 AIRPLANES, AIRSHIPS, AIRCKAFT ENGINES

Ceiling: Absolute. — The maximum height above sea level which a given aircraft can approach asymptotically, assuming standard air conditions.

Service. — The height above sea level at which a given aircraft ceases to rise at a rate higher than a small specified one (100 feet per minute in United States Air Service). This specified rate may be different in the services of different countries.

Cell. — The entire structure of the wings and wing trussing on one side of the fuselage of an airplane, or between fuselage or nacelles, where there are more than one.

Center of pressure of an aerofoil section. — The point in the chord of an aerofoil section, prolonged if necessary, through which at any given attitude the line of action of the resultant air force passes.

Chord:

Of an aerofoil section. — The fine of a straightedge brought into contact with the lower surface of the section at two points. In the case of an aerofoil having double convex camber the straight line joining the leading and trailing edges. (These edges may be defined, for this purpose, as the two points in the section which are farthest apart. (Fig. 9.) Length. — The length of the projection of the aerofoil section on its chord.

Chord, mean, of a wing. — The quotient obtained by dividing the wing area by the extreme dimension of the wing projection at right angles to the chord.

Climb, rate of. — The vertical component of the air speed of an aircraft; i.e., its vertical velocity with reference to the air.

Cockpit. — The open spaces in which the pilot and passengers are accommodated. A cockpit is never completely housed in.

Concentration ring: Airship. — A metal ring to which several rigging lines are brought from the envelope and from which one or more lines also lead to the car.

Free balloon. — A hoop to which are attached the ropes suspending the basket and to which the net is also secured.

Parachute. — A hoop to which the rigging of the parachute is attached and also the line sustaining the passenger.

Consumption per B.H.P. hour. — The quantity of fuel or oil consumed per hour by an engine running at ground level divided by the brake horsepower developed, unless specifically stated otherwise.

Control column or yoke. — A control lever with a rotatable wheel mounted at its upper end. (See Control stick.) Pitching is controlled by fore-and-aft movement of the column; rolling, by rotation of the wheel. " Wheel control" is that type of control in which such a column or yoke is used.

Control stick. — The vertical lever by means of which certain of the principal controls of an airplane are operated. Pitching is controlled by a fore-and-aft movement of the stick, rolling by side-to-side movement. "Stick control" is that type of control in which such a stick is used.

Controls. — A general term applying to the means provided to enable the pilot to control the speed, direction of flight, attitude, and power of an aircraft.

Cord. — A species of wire made up of several strands (usually 7) twisted together as in a rope, each of the strands, in turn, being made up of several (usually 19) individual wires.

Cowling. — The metal covering which houses the engine and sometimes a portion of the fuselage or nacelle as well.

Critical angle. — (See Angle.)

Cross-wind force. — The component perpendicular to the lift and to the drag of the total force on an aircraft due to the air through which it moves.

Crow's-foot. — A system of diverging short ropes for distributing the pull of a single rope.

Damping factor. — The percentage of damping in one period.

Dead load — (See Load.)

Dihedral angle. — (See Angle.)

Disk area. — The total area swept by a propeller, i.e., the area of a circle having a diameter equal to the propeller diameter.

Dischargeable weight. — The excess of the gross buoyancy over the dead load, the crew and such items of equipment as are essential to enable an airship to fly and land safely.

Dive. — A steep glide.

Divergence. — A disturbance which increases without oscillation.

Dope, airplane. — A general term applied to the material used in treating the cloth surface of airplane members to increase strength, produce tautness, and act as a filler to maintain airtightness.

Downwash angle. — (See Angle.)

Drag. — The component parallel to the relative wind of the total force on an aerofoil or aircraft due to the air through which it moves.

In the case of an airplane, that part of the drag due to the wings is called "wing resistance;" that due to the rest of the airplane is called " structural" or " parasite resistance."

Drag rope. — The rope dropped by an airship in order to allow it to be secured by a landing party.

Drag strut. — A compression member of the internal bracing system of an aerofoil.

Drag wires. — (See Wires.)

Drift. — The angular deviation from a set course over the earth, due to cross currents of wind, hence, " drift meter."

Drift meter. — An instrument for the measurement of the angular deviation of an aircraft from a set course, due to cross winds.

Drip flap. — A strip of fabric attached by one edge to the envelope of an aerostat so that rain runs off its free edge instead of dripping into the basket or car. The drip flap assists also to keep the suspension ropes dry and nonconducting.

Dry weight. — The weight of an engine, including carburetors, propeller-hub assembly, and ignition system complete, but excluding exhaust manifolds.

Dynamic factor. — The ratio between the load carried by any part of an aircraft when accelerating or when otherwise subjected to abnormal conditions and the load carried in normal flight.

Dynamic lift. — (See Lift.)

Effective pitch.— (See Pitch.)

Elevator. — A movable auxiliary surface of an airplane, usually attached to the tail plane, the function of which is to impress a pitching moment on the aircraft. (Fig. 10.)

Empennage. — Same as tail unit.

Envelope. — The outer covering of a rigid airship; or, in the case of a balloon or a nonrigid airship, the bag which contains the gas.

Equator. — The largest horizontal circle of a spherical balloon.

Fabric, balloon. — The finished material, usually rubberized, of which balloon or airship envelopes are made.

AIRPLANES, AIRSHIPS, AIRCBAFT ENGINES

CkoTiet length.-

Pig- ii

Biased. — Plied fabric in which the threads of the plies are

at an angle to each other.

Parallel. — Plied fabric in which the threads of the plies are parallel to each other.

Factor, dynamic. — (See Dynamic factor.)

Factor of safety. — The ratio of the ultimate strength of a member to the maximum possible load occurring under conditions specified.

Fairing. — A member whose primary function is to produce a smooth outline and to reduce head resistance or drag.

Fins. — Small stationary surfaces, substantially vertical, attached to different parts of aircraft, in order to promote stability; for example, tail fins, skid fins, etc. Fins are sometimes adjustable. (Fig. 10.) Skid fins. — Fore and aft vertical surfaces, usually placed well out toward the tips of the upper plane, designed to provide the vertical keel-surface required for stability.

Fins, kite balloon. — The air inflated lobes intended to keep the balloon headed into the wind.

Fire wall. — A metal plate, so set as to isolate from the engine the other parts of the airplane structure, and thus to reduce the risk from a backfire.

Fitting. — A generic term for any small metal part used in the structure of an airplane.

Flight path. — The path of the center of gravity of an aircraft with reference to the ear^h.

Float. — A completely inclosed water-tight structure attached to an aircraft in order to furnish it buoyancy when in contact with the surface of the water. In float seaplanes the crew is carried in a fuselage or nacelle separate from the float.

Floating seaplane. — (See Seaplane.)

Flotation gear. — An emergency landing gear attached to an airplane, which will permit of safe landing on the water and provide buoyancy when resting on the surface of the water.

Flying boat. — (See Seaplane.)

Free-flight testing. — The conduct of special flight tests of a scientific nature, as contrasted with performance testing.

Full load.— (See Load.)

Fuselage. — The elongated structure, of approximately steamline form, to which are attached the wings and tail unit of an airplane. In general, it is designed to hold the passengers.

Fuselage, length of. — The distance from the nose of the fuselage (including the engine bed and radiator, if present) to the after end of the fuselage, not including the control and stabilizing surfaces.

Gap. — The shortest distance between the planes of the chord of the upper and lower wings of a biplane, measured along a line perpendicular to the chord of the upper wing at any designated point of its entering edge. (Fig.

no

Geometrical pitch. — (See Pitch.)

Glide, to. — To descend at a normal angle of attack without engine power sufficient for level flight, the propeller thrust being replaced by a component of gravity along the line of flight.

Glider. — A form of aircraft similar to an airplane, but without any power plant. Gliders are used chiefly for sport.

Gliding angle. — (See Angle.)

Gore. — The portion of the envelope of a balloon or airship included between two adjacent meridian seams.

Gross buoyancy. — (See Buoyancy.)

Ground cloth. — Canvas placed on the ground to protect a balloon.

Ground speed. — (See Speed.)

Handling truck. — A truck, mounted on wheels or sliding on ways, on which airplanes or seaplanes may be placed to facilitate moving them about and carrying them to and from their hangars.

Hangar. — A shelter for housing aircraft.

Helicopter. — A form of aircraft whose support in the air is derived from the vertical thrust of propellers.

Hog (Airship). — A distortion of the envelope in which the axis becomes convex upward or both ends droop.

Horn. — The operating lever of a control sufrace of an aircraft, e.g., aileron horn, rudder horn, elevator horn.

Horsepower of an engine, maximum. — The maximum horsepower which can be safely maintained for periods not less than five minutes.

Horsepower of an engine, normal. — The highest horsepower which can be safely maintained for long periods.

Hull (airship). — The main structure of a rigid airship, consisting of a covered elongated framework which incloses the gas bags and which supports the cars and equipment.

Hull (seaplane). — The portion of a boat seaplane which furnishes buoj^ancy when in contact with the surface of the water, to which the main supporting surfaces and other parts are attached, and which contains accommodations for the crew.

Incidence, angle of. — (See Angle.)

Inclinometer :

Absolute. — An instrument giving the attitude of an aircraft with reference to true gravity.

Relative. — An instrument giving the attitude of an aircraft with reference to apparent gravity. Such instruments are sometimes incorrectly referred to as banking indicators.

Indicator, air-speed. — An anemometer mounted on an aircraft for the purpose of indicating the speed of the aircraft.

True air-speed indicator. — An instrument, usually working on the principle of the Biram or Robinson anemometers, which gives the true air speed, independent of density.

Apparent air-speed indicator. — An instrument, usually dependent on pressure measurements, the readings of which vary with the density of the air.

Indraft. — The drawing in of air from in front of a propeller by the action of the rotating blades. The indraft velocity relative to the propeller is somewhat higher than that of the undisturbed air at most points of the propeller disk.

Inspection window. — A small transparent window in the envelope of a balloon or in the wing of an airplane to allow inspection of the interior.

Jackstay. — A longitudinal rigging provided to maintain the correct distance between the heads of various riggings on an airship.

Keel. — A member or assembly of members which provides longitudinal strength to an airship of rigid or semirigid type. In the case of a rigid airship the keel is usually an elaborately trussed girder and may be inclosed within the envelope or may project beyond (usually below) the regular cross-sectional form of the envelope. Articulated. — A keel made up of a series of members hinged together at their ends.

King post. — The main compression member of a trussing system applied to a member subject to bending. (Fig. 4.)

Kite. — A form of aircraft without other propelling means than the towline pull, whose support is derived from the force of the wind moving past its surface.

Kite balloon. — (See Balloon.)

Laminated wood. — Wooden parts made up by gluing or

otherwise fastening together individual wood planks or laminations with the grain substantially parallel.

Landing angle. — (See Angle.)

Landing field. — A field of such a nature as to permit of airplanes landing or taking off.

Landing gear. — The understructure of an aircraft designed to carry the load when in contact with the land or water.

Leading edge. — The foremost edge of an aerofoil or propeller blade.

Length, chord. — (See Chord.)

Length, fuselage. — (See Fuselage.)

Length, over-all. — (See Over-all.)

Lift. — The component of the total air force which is perpendicular to the relative wind and in the plane of symmetry. It must be specified whether this applies to a complete aircraft or parts thereof. (In the case of an airship this is often called "dynamic lift.")

Lift wires. — (See Wires.)

Load : Dead. — The structure, power plant, and essential accessories of an aircraft. Included in this are the water in the radiator, tachometer, thermometer, gauges, air-speed indicators, levels, altimeter, compass, watch and hand starter, and also, in the case of an aerostat, the amount of ballast which must be carried to assist in making a safe landing.

Full. — The total weight of an aircraft when loaded to the maximum authorized loading of that particular type. Useful. — The excess of the full load over the dead load of the aircraft itself. Therefore useful load includes the crew and passengers, oil and fuel, ballast, electriclight installation, chart board, detachable gun mounts, bomb storage and releasing gear, wireless apparatus, etc.

Load factor. — The ratio of the ultimate strength of a member to the load under horizontal steady rectilinear flight conditions.

Lobes. — Inflated bags at the stern of an elongated balloon, designed to give it directional stability. Also used to denote the sections into which the envelope is sometimes (e.g., in the Astra-Torres) divided by the tension of the internal rigging.

Longeron. — A fore-and-aft member of the framing of an airplane fuselage or nacelle, usually continuous across a number of points of support. (Fig. 12.)