Podcast
Questions and Answers
During a steady climb, how does lift relate to the weight vector?
During a steady climb, how does lift relate to the weight vector?
- Lift always exceeds the weight vector to maintain a positive climb angle.
- Lift is perpendicular to the airspeed vector and, with thrust, determines the climb angle.
- Lift equals the weight vector, and the flight path angle depends only on drag and thrust.
- Lift counteracts the perpendicular component of weight relative to the flight path, while thrust adjusts for the parallel component. (correct)
For an aircraft with constant power available, if aerodynamic drag is proportional to the square of airspeed ($D \propto V^2$), how does the required power change with airspeed?
For an aircraft with constant power available, if aerodynamic drag is proportional to the square of airspeed ($D \propto V^2$), how does the required power change with airspeed?
- Cubically (correct)
- Linearly
- Quadratically
- Exponentially
An aircraft weighs 200,000 kg, with 20% of its weight being fuel. The remaining weight is split equally between empty weight and payload. If the empty weight is reduced by 5%, what is the new total weight of the aircraft?
An aircraft weighs 200,000 kg, with 20% of its weight being fuel. The remaining weight is split equally between empty weight and payload. If the empty weight is reduced by 5%, what is the new total weight of the aircraft?
- 196,000 kg (correct)
- 190,000 kg
- 195,000 kg
- 192,500 kg
Why does the propulsive efficiency of a jet engine primarily depend on the ratio of flight velocity ($V$) to jet exhaust velocity ($V_j$)?
Why does the propulsive efficiency of a jet engine primarily depend on the ratio of flight velocity ($V$) to jet exhaust velocity ($V_j$)?
In which years were Sputnik launched and the first moon landing achieved, respectively?
In which years were Sputnik launched and the first moon landing achieved, respectively?
What is NOT typically considered an advantage of using constellations of satellites compared to using a single satellite in geostationary orbit for communication purposes?
What is NOT typically considered an advantage of using constellations of satellites compared to using a single satellite in geostationary orbit for communication purposes?
Which formula accurately describes the thrust ($T$) produced by a rocket engine, where $\dot{m}$ is the mass flow rate of the expelled propellant and $v_e$ is the exhaust velocity?
Which formula accurately describes the thrust ($T$) produced by a rocket engine, where $\dot{m}$ is the mass flow rate of the expelled propellant and $v_e$ is the exhaust velocity?
What is the primary function of the upper stage of a rocket?
What is the primary function of the upper stage of a rocket?
In the Tsiolkovsky rocket equation, what does the 'mass fraction' primarily represent?
In the Tsiolkovsky rocket equation, what does the 'mass fraction' primarily represent?
Which statement accurately describes Kepler's Second Law of Planetary Motion?
Which statement accurately describes Kepler's Second Law of Planetary Motion?
How does the flight path angle ($\gamma$) relate to lift and weight during a descent?
How does the flight path angle ($\gamma$) relate to lift and weight during a descent?
If the drag coefficient ($C_d$) remains constant, how does doubling the airspeed ($V$) affect the aerodynamic drag ($D$) on an aircraft?
If the drag coefficient ($C_d$) remains constant, how does doubling the airspeed ($V$) affect the aerodynamic drag ($D$) on an aircraft?
Prior to a 5% reduction in the empty weight the payload and empty weight were equal. What percentage of the original total aircraft weight constitutes the new empty weight?
Prior to a 5% reduction in the empty weight the payload and empty weight were equal. What percentage of the original total aircraft weight constitutes the new empty weight?
How does increasing the jet exhaust velocity ($V_j$) relative to the aircraft's flight velocity ($V$) affect the propulsive efficiency of a jet engine, assuming all other factors remain constant?
How does increasing the jet exhaust velocity ($V_j$) relative to the aircraft's flight velocity ($V$) affect the propulsive efficiency of a jet engine, assuming all other factors remain constant?
What is a key advantage of geostationary satellites compared to satellite constellations for communication purposes?
What is a key advantage of geostationary satellites compared to satellite constellations for communication purposes?
Flashcards
Lift and Weight Vectors in Climbs/Descents
Lift and Weight Vectors in Climbs/Descents
Lift is perpendicular to the airspeed vector. It counteracts the weight component perpendicular to the flight path. Thrust adjusts the parallel weight component to determine flight path angle (γ).
Power Required vs. Airspeed Relationship
Power Required vs. Airspeed Relationship
The power required increases cubically with airspeed. Power Required (PR) = V^3.
Calculating New Total Weight After Weight Reduction
Calculating New Total Weight After Weight Reduction
New total weight = New empty weight + Payload + Fuel Weight
Jet Engine Propulsive Efficiency
Jet Engine Propulsive Efficiency
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Satellites Constellations Advantages
Satellites Constellations Advantages
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Rocket Engine Thrust Formula
Rocket Engine Thrust Formula
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Purpose of Rocket Upper Stage
Purpose of Rocket Upper Stage
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Mass Fraction (Tsiolkovsky Equation)
Mass Fraction (Tsiolkovsky Equation)
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Kepler's Second Law of planetary motion
Kepler's Second Law of planetary motion
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Study Notes
- The relationship between lift and weight vectors affects the flight path angle during a steady climb or descent.
- Lift is perpendicular to the airspeed vector.
- Lift counteracts the component of weight perpendicular to the flight path.
- Thrust adjusts for the parallel component of weight to determine the flight path angle (γ).
- Lift is always perpendicular to the flight path.
- In level flight, lift equals weight; during a climb or descent (at an angle γ), lift balances out the perpendicular component of weight.
- In a steady climb, the lift vector does not exceed the weight.
- Lift balances the perpendicular component of weight.
- Thrust provides the additional force needed to overcome both drag and the weight component along the flight path.
- Thrust plays a role in counteracting the parallel weight component.
Propeller-Driven Aircraft and Airspeed
- When an aircraft with a propeller-driven engine has a performance diagram showing constant power available at different airspeeds and with aerodynamic drag (D) modeled as D = Cd * 0.5 * ρ * V², the power required increases cubically with airspeed.
- Drag increases quadratically with airspeed (D ∝ V²).
- Power required formula: PR = D V
- Substituting D ∝ V²: PR = V² * V = V³
Aircraft Weight Calculation
- Given an aircraft with a total weight of 200,000 kg, where 20% is fuel and the rest is divided equally between empty weight and payload, achieving a 5% reduction in empty weight leads to a new total weight of 196,000 kg. Total aircraft weight: 200,000kg
- Fuel weight: 20% of 200,000kg = 40,000kg
- Remainder (empty weight + payload) = 200,000kg - 40,000kg = 160,000kg
- Empty weight = Payload = 160,000kg / 2 = 80,000kg
- New empty weight after 5% reduction: 80,000kg - (0.05 * 80,000kg) = 76,000kg
- New total weight = 76,000kg (new empty weight) + 80,000kg (payload) + 40,000kg (fuel) = 196,000kg
Jet Engine Propulsive Efficiency
The propulsive efficiency of a jet engine depends only on the ratio of the aircraft velocity to the jet velocity (V/Vj).
- Propulsive efficiency shows how kinetic energy is converted into useful work for moving the aircraft.
- Higher propulsive efficiency means a larger portion of available energy contributes to thrust.
- If V ≈ Vj, exhaust velocity is nearly matched to aircraft speed (more energy goes to forward motion and provides higher efficiency).
- If V << Vj, most of the energy remains in the exhaust and lowers efficiency.
Sputnik & Moon Landing Dates
- Sputnik was launched in 1957.
- The moon landing occurred in 1969.
Satellite Constellations
- Lower bandwidth capability isn't an advantage of using satellite constellations, as opposed to a single satellite in geostationary orbit for communication purposes.
- A smaller satellite size results from a constellation approach due to space, power, and pointing limitations.
- Bandwidth of an antenna is heavily influenced by its size so large bandwidth capability is not an advantage of utilizing a constellation of satellites
Rocket Engine Thrust Formula
- The formula that correctly describes the thrust of a rocket engine is T = ṁve
- Thrust (T) is measured in Newtons (N).
- ṁ represents mass flow rate of expelled propellant (kg/s).
- ve is exhaust velocity (m/s).
- Rockets generate thrust by ejecting mass at high velocity, creating an equal and opposite reaction force.
Upper Stage of a Rocket
- The upper stage of a rocket provides the final delta-V to the payload for injection into the target orbit.
Tsiolkovsky Rocket Equation
- In the Tsiolkovsky rocket equation, the mass fraction is the ratio of the propellant mass to the total initial mass of the rocket. Δv = ve * ln(m0/mf)
- m0 = original mass of the rocket
- mf = final mass of the rocket
- The mass fraction (m0/mf ) is the ratio of the mass fully empty from propellant to the mass of the rocket fully fueled.
Kepler's Second Law of Planetary Motion
- A line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time.
- As a planet orbits the Sun, its speed increases as it gets closer and slows down as it moves farther to maintain constant angular momentum.
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