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Thrust-to-Weight Ratio

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine ... more

Wing loading - turning radius

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... more

Thrust-to-Weight Ratio - Propeller-driven aircraft

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine ... more

Lift-to-Drag Ratio

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving ... more

Lift-to-Drag Ratio - with wetted aspect ratio

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving ... more

Zero-Lift Drag Coefficient

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving ... more

Thrust to Propulsive Power

Thrust is a reaction force described quantitatively by Newton’s second and third laws.
A very common question is how to contrast the thrust ... more

Glide Ratio

Gliding flight is heavier-than-air flight without the use of thrust; the term volplaning also refers to this mode of flight in animals. It is employed by ... more

Wind loading - takeoff speed

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... more

Sears–Haack body (Wave Drag related to the maximum Radius)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Sears–Haack body (Wave Drag related to the Volume)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Wing loading - upward acceleration

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... more

Sears–Haack body (Drag Coefficient related to the Volume)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Sears–Haack body (Drag Coefficient related to the maximum Radius)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Supersonic/Hypersonic Lift-to-Drag Ratio

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving ... more

Ideal rocket equation (Tsiolkovsky rocket equation)

The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a ... more

Worksheet 289

Prior to manned space flights, rocket sleds were used to test aircraft, missile equipment, and physiological effects on human subjects at high speeds. They consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force exerted by each rocket, called its thrust T , for the four-rocket propulsion system shown in the Figure below. The sled’s initial acceleration is 49 m/s 2, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N.

A sled experiences a rocket thrust that accelerates it to the right.Each rocket creates an identical thrust T . As in other situations where there is only horizontal acceleration, the vertical forces cancel. The ground exerts an upward force N on the system that is equal in magnitude and opposite in direction to its weight,w.The system here is the sled, its rockets, and rider, so none of the forces between these objects are considered. The arrow representing friction ( f ) is drawn larger than scale.
Assumptions: The mass of the Sled remains steady throughout the operation

Strategy

Although there are forces acting vertically and horizontally, we assume the vertical forces cancel since there is no vertical acceleration. This leaves us with only horizontal forces and a simpler one-dimensional problem. Directions are indicated with plus or minus signs, with right taken as the positive direction. See the free-body diagram in the figure.

Solution

Since acceleration, mass, and the force of friction are given, we start with Newton’s second law and look for ways to find the thrust of the engines. Since we have defined the direction of the force and acceleration as acting “to the right,” we need to consider only the magnitudes of these quantities in the calculations. Hence we begin with

Force (Newton's second law)

Fnet is the net force along the horizontal direction, m is the rocket’s mass and a the acceleration.

We can see from the Figure at the top, that the engine thrusts add, while friction opposes the thrust.

Subtraction

Tt is the total thrust from the 4 rockets, Fnet the net force along the horizontal direction and Ff the force of friction.

Finally, since there are 4 rockets, we calculate the thrust that each one provides:

Division

T is the individual Thrust of each engine, b is the number of rocket engines

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Equivalent airspeed (in function of Mach number)

Equivalent airspeed (EAS) is the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is ... more

True Airspeed - Low-speed flight

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass ... more

Water Rocket - peak height

A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water ... more

True Airspeed - High-speed flight (simplified, in knots)

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass ... more

Drag coefficient

Drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) refers to forces acting ... more

Propellant mass fraction

In aerospace engineering, the propellant mass fraction is the portion of a vehicle’s mass which does not reach the destination, usually used as a ... more

Terminal velocity (under buoyancy force)

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity ... more

Specific Impulse by weight - with mass flow rate

Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more

Equivalent airspeed (in function of dynamic pressure)

Equivalent airspeed (EAS) is the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is ... more

Power in a reference system(aerodynamic drag)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Thrust (with cross section area)

Thrust is a reaction force described quantitatively by Newton’s second and third laws. When a system expels or accelerates mass in one direction, the ... more

True Airspeed - High-speed flight

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass ... more

Lift coefficient (for an airfoil section)

The lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the density of the fluid around the body, its ... more

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