ME 239: Rocket Propulsion. Forces Acting on a Vehicle in an Atmosphere (Follows Section 4.2) J. M. Meyers, PhD

Transcription

1 ME 239: Rocket Propulsion Forces Acting on a Vehicle in an Atmosphere (Follows Section 4.2) J. M. Meyers, PhD 1

2 Commonly acting forces on a vehicle flying in a planetary atmosphere: Thrust Aerodynamic Forces(Lift, and Drag, ) Weight(due to gravity) Smaller forces exist but are generally neglected for most applications: Wind Solar radiation pressure(srp) Solar sail applications 2

3 Force produced by rocket, propeller, or jet engine Thrust Normally acts along rocket center of mass and through axis unless used for maneuvering and attitude adjustment Ignoring transients(start-up and shut-down): 3

4 Aerodynamic Lift Lift,,istheaerodynamicactinginadirectionnormaltoflightpath This owes to aerodynamic lifting forces of body and aerodynamic surfaces Lift Dynamic Pressure Lift Coefficient lift[n] liftcoefficient[-] density[kg/m 3 ] Typicalsurfaceorcross-sectionalarea[m 2 ] vehicle velocity[m/sec] dynamicpressure[n/m 2 ] 4

5 Aerodynamic Lift Lift coefficient is a dimensionless, area and dynamic pressure normalized form of lift Foraircraftthearea usedisthewingwettedarea For wingless missiles or space launch vehicles it is customary to use the cross-section area of the vehicle body Lift coefficient will depend on Vehicle configuration Flight Mach#(for higher speeds this is dependency is more relevant) Angle of attack, 5

6 Aerodynamic Lift Variation of lift coefficient with Mach number of the German V-2 missile at several angles of attack. based on body cross-sectional area jet off exhaust plume effects neglected 6

7 Aerodynamic Drag Drag,, is the aerodynamic acting in a direction opposite to flight path Duetoresistanceofthebodytomotioninafluid Drag Dynamic Pressure Drag Coefficient lift[n] liftcoefficient[-] density[kg/m 3 ] Typicalsurfaceorcross-sectionalarea[m 2 ] vehicle velocity[m/sec] dynamicpressure[n/m 2 ] 7

8 Aerodynamic Drag Just as with the lift coefficient: Lift coefficient is a dimensionless, area and dynamic pressure normalized form of lift Foraircraftthearea usedisthewingwettedarea For wingless missiles or space launch vehicles it is customary to use the cross-section area of the vehicle body Drag coefficient will depend on Vehicle configuration Flight Mach#(for higher speeds this is dependency is more relevant) Angle of attack, 8

9 Aerodynamic Drag Variation of drag coefficient with Mach number of the German V-2 missile at several angles of attack. based on body cross-sectional area jet off exhaust plume effects neglected 9

10 Aerodynamic Drag Wave Drag Drag data for German V-2 supersonic rocket RegionbetweenMach0.85andMach1.15isknownasthetransonicregion Here strong unsteady aerodynamic forces can develop Increased transonic aerodynamic loads(increased!!!) have led to structural failures of flight vehicles 10

11 Some common forms of drag: Skin Friction Drag: Caused by the viscosity of the atmosphere. Varies widely depending on the flow conditions around the body and surface roughness of skin. Primary drag at low Re but normally small fraction of overall drag contribution at higher Mach #. Base Drag: caused by the boundary layer coming off of the back of the cylinder and mixing with the stagnated air behind the base Pressure Drag: Normally the largest drag component. Highly influenced by viscous behavior. Resulting drag a result of adverse pressure gradients on the body like flow separation or shocks. Transonic drag rise is a pressure attributed drag phenomenon. 11

12 Transonic Drag Rise (Wave Drag) Aerodynamic Drag Transonic regime begins when the critical Mach number is achieved Transonic flow is characterized by mixed regions of locally subsonic and supersonic flow occurring over a moving body at Mach numbers near unity wave drag is due to the unstable formation of shock waves which transforms a considerable part of the available propulsive energy into heat Additional loss is due to induced separation of the flow from the airplane surfaces Once a supersonic flow has been established the flow stabilizes and the drag coefficient is reduced Increased Mach number increases shock strength and pushes shock aft 12

13 Area Rule: Aerodynamic Drag Drag at high speeds is a function of an aircraft s total cross-sectional area (essentially, the thickness of the fuselage). Projections from the fuselage (i.e. aerodynamic surfaces) increase a plane's cross section Narrowing the body where aerodynamic surfaces attach reduces drag. Note: Area ruling was more commonly done in the days of first supersonic flights as engine power ratings were relatively low and not capable of pushing the vehicle through this drag spike 13

14 Aerodynamic Drag Proper area ruling can help reduce transonic drag rise 14

15 Based on gravitational attraction Gravitational Force (Weight) Gravity forces pull vehicle in direction of mass center of attracting body If Earth is only attractive body we can consider this force as weight Keep in mind that gravity varies w.r.t. attitude. If 0 is gravity at the surface of a spherical Earth with effective radius of 0 the gravitational force w.r.t. altitude is then: h DistancefromEarthcentertoEarthsurface( km) Distance from Earth center to vehicle location gravityatearthsurface( m/sec 2 ) gravity at vehicle location h distance between Earth surface and vehicle location(aka altitude) 15