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Velocity for Maximizing Range given Range for Jet Aircraft Formula

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Velocity at Maximum Lift to Drag Ratio is the velocity when the ratio of lift and drag coefficient is maximum in value. Basically considered for the cruise phase. Check FAQs

V L/D(max) = \frac{R \cdot c}{LDmax ratio \cdot \ln (\frac{W i}{W f})}

V_L/D(max) - Velocity at Maximum Lift to Drag Ratio?R - Range of Aircraft?c - Power Specific Fuel Consumption?LDmax_ratio - Maximum Lift-to-Drag Ratio of Aircraft?W_i - Weight of Aircraft at Beginning of Cruise Phase?W_f - Weight of Aircraft at End of Cruise Phase?

Velocity for Maximizing Range given Range for Jet Aircraft Example

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Here is how the Velocity for Maximizing Range given Range for Jet Aircraft equation looks like with Values.

Here is how the Velocity for Maximizing Range given Range for Jet Aircraft equation looks like with Units.

Here is how the Velocity for Maximizing Range given Range for Jet Aircraft equation looks like.

42.7942 = \frac{1000 \cdot 0.6}{19.7 \cdot \ln (\frac{514}{350})}

42.7942kn = \frac{1000km \cdot 0.6kg/h/W}{19.7 \cdot \ln (\frac{514kg}{350kg})}

42.7942 = \frac{1000 \cdot 0.6}{19.7 \cdot \ln (\frac{514}{350})}

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Velocity for Maximizing Range given Range for Jet Aircraft Solution

Follow our step by step solution on how to calculate Velocity for Maximizing Range given Range for Jet Aircraft?

FIRST Step Consider the formula

V L/D(max) = \frac{R \cdot c}{LDmax ratio \cdot \ln (\frac{W i}{W f})}

Next Step Substitute values of Variables

∴

V L/D(max) = \frac{1000km \cdot 0.6kg/h/W}{19.7 \cdot \ln (\frac{514kg}{350kg})}

Next Step Convert Units

∴

V L/D(max) = \frac{1E+6m \cdot 0.0002kg/s/W}{19.7 \cdot \ln (\frac{514kg}{350kg})}

Next Step Prepare to Evaluate

∴

V L/D(max) = \frac{1E+6 \cdot 0.0002}{19.7 \cdot \ln (\frac{514}{350})}

Next Step Evaluate

∴

V L/D(max) = 22.0152344416059m/s

Next Step Convert to Output's Unit

∴

V L/D(max) = 42.7941922191042kn

LAST Step Rounding Answer

∴

V L/D(max) = 42.7942kn

Velocity for Maximizing Range given Range for Jet Aircraft Formula Elements

Variables

Functions

Velocity at Maximum Lift to Drag Ratio

Velocity at Maximum Lift to Drag Ratio is the velocity when the ratio of lift and drag coefficient is maximum in value. Basically considered for the cruise phase.

Symbol: V_L/D(max)

Measurement: SpeedUnit: kn

Note: Value should be greater than 0.

Formulas to find Velocity at Maximum Lift to Drag Ratio

Range of Aircraft

Range of Aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.

Symbol: R

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Range of Aircraft

Power Specific Fuel Consumption

Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.

Symbol: c

Measurement: Specific Fuel ConsumptionUnit: kg/h/W

Note: Value should be greater than 0.

Formulas to find Power Specific Fuel Consumption

Maximum Lift-to-Drag Ratio of Aircraft

Maximum Lift-to-Drag Ratio of Aircraft refers to the highest ratio of lift force to drag force. It represents the optimal balance between lift and drag for maximum efficiency in level flight.

Symbol: LDmax_ratio

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Maximum Lift-to-Drag Ratio of Aircraft

Weight of Aircraft at Beginning of Cruise Phase

Weight of Aircraft at Beginning of Cruise Phase is the weight of the plane just before going to cruise phase of the mission.

Symbol: W_i

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at Beginning of Cruise Phase

Weight of Aircraft at End of Cruise Phase

Weight of Aircraft at End of Cruise Phase is the weight before the loitering/descent/action phase of the mission plan.

Symbol: W_f

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at End of Cruise Phase

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Preliminary Design category

Go Preliminary Take Off Weight Built-up for Manned Aircraft

DTW = PYL + OEW + FW + W c

Go Fuel Fraction

F f = \frac{FW}{DTW}

Go Preliminary Take off Weight Built-Up for Manned Aircraft given Fuel and Empty Weight Fraction

DTW = \frac{PYL + W c}{1 - F f - E f}

Go Optimum Range for Jet Aircraft in Cruising Phase

R = \frac{V L/D(max) \cdot LDmax ratio}{c} \cdot \ln (\frac{W i}{W f})

How to Evaluate Velocity for Maximizing Range given Range for Jet Aircraft?

Velocity for Maximizing Range given Range for Jet Aircraft evaluator uses Velocity at Maximum Lift to Drag Ratio = (Range of Aircraft*Power Specific Fuel Consumption)/(Maximum Lift-to-Drag Ratio of Aircraft*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)) to evaluate the Velocity at Maximum Lift to Drag Ratio, The Velocity for Maximizing Range given Range for Jet Aircraft refers to the initial velocity at which a projectile should be launched to achieve the greatest horizontal distance traveled under the influence of gravity, this formula for calculating the velocity required for maximizing the lift-to-drag ratio of an aircraft, considering various parameters such as range, power specific fuel consumption, aircraft weight, and the maximum lift-to-drag ratio. Velocity at Maximum Lift to Drag Ratio is denoted by V_L/D(max) symbol.

How to evaluate Velocity for Maximizing Range given Range for Jet Aircraft using this online evaluator? To use this online evaluator for Velocity for Maximizing Range given Range for Jet Aircraft, enter Range of Aircraft (R), Power Specific Fuel Consumption (c), Maximum Lift-to-Drag Ratio of Aircraft (LDmax_ratio), Weight of Aircraft at Beginning of Cruise Phase (W_i) & Weight of Aircraft at End of Cruise Phase (W_f) and hit the calculate button.

FAQs on Velocity for Maximizing Range given Range for Jet Aircraft

What is the formula to find Velocity for Maximizing Range given Range for Jet Aircraft?

The formula of Velocity for Maximizing Range given Range for Jet Aircraft is expressed as Velocity at Maximum Lift to Drag Ratio = (Range of Aircraft*Power Specific Fuel Consumption)/(Maximum Lift-to-Drag Ratio of Aircraft*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)). Here is an example- 83.60895 = (1000000*0.000166666666666667)/(19.7*ln(514/350)).

How to calculate Velocity for Maximizing Range given Range for Jet Aircraft?

With Range of Aircraft (R), Power Specific Fuel Consumption (c), Maximum Lift-to-Drag Ratio of Aircraft (LDmax_ratio), Weight of Aircraft at Beginning of Cruise Phase (W_i) & Weight of Aircraft at End of Cruise Phase (W_f) we can find Velocity for Maximizing Range given Range for Jet Aircraft using the formula - Velocity at Maximum Lift to Drag Ratio = (Range of Aircraft*Power Specific Fuel Consumption)/(Maximum Lift-to-Drag Ratio of Aircraft*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)). This formula also uses Natural Logarithm (ln) function(s).

Can the Velocity for Maximizing Range given Range for Jet Aircraft be negative?

No, the Velocity for Maximizing Range given Range for Jet Aircraft, measured in Speed cannot be negative.

Which unit is used to measure Velocity for Maximizing Range given Range for Jet Aircraft?

Velocity for Maximizing Range given Range for Jet Aircraft is usually measured using the Knot[kn] for Speed. Meter per Second[kn], Meter per Minute[kn], Meter per Hour[kn] are the few other units in which Velocity for Maximizing Range given Range for Jet Aircraft can be measured.

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Velocity for Maximizing Range given Range for Jet Aircraft Formula

Velocity for Maximizing Range given Range for Jet Aircraft Example

Velocity for Maximizing Range given Range for Jet Aircraft Solution

Velocity for Maximizing Range given Range for Jet Aircraft Formula Elements

Other formulas in Preliminary Design category

How to Evaluate Velocity for Maximizing Range given Range for Jet Aircraft?

FAQs on Velocity for Maximizing Range given Range for Jet Aircraft

Variable Name