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These are my data;

  • $C_{L_0} = 0.4$
  • $C_{L_{\alpha}} = 5.7$
  • $C_{L_{minD}} = 0.14$
  • $C_{D_{min}} = 0.022$
  • $k = 0.035$
  • $\alpha_{stall} = 15$
  • $S_{ref} = 20m^2$

Mass Data

  • $W_{total} = 2500 \text{ kg}$
  • $W_{fuel} = 800 \text{ L}$
  • $\rho_{fuel} = 800 \text{ kg/m}^3$
  • $mass_{fuel} = (1/1000) \cdot W_{fuel} \cdot \rho_{fuel} \text{ kg}$ , 1/1000 l from coverting into m^3
  • $g = 9.807 \text{m/s}^2$ gravity

Propulsion Data

  • Engine_type = "Internal Combustion Engine"
  • Propeller_type = "Constant Speed Propeller"
  • S_prop = 1.9 # m^2
  • n_prop = 0.8 # %80
  • SFC_takeoff = 0.28 # kg/kW/h
  • P_takeoff = 400 # HP
  • P_maxCont = 350 # HP
  • SFC_maxCont = 0.25 # kg / kW /h
  • P_cruise = 280 # HP
  • SFC_cruise = 0.2 # kg/kw/h

My main purpose is calculate maximum range and endurance at constant velocity and altitude. So that I have started to calculate $C_{L} = C_{L_0} + alpha * C_{L_\alpha}$ to find $V_{stall}$ and $C_{L_{max}}$. Well I have different $P_{cruise}$ and $P_{takeoff}$. I am uncertain how to proceed because I didn't decide, or am uncertain how to decide, which one of speeds I need to use TAS, or $V_{cruise}$. I decided to calculate CD by using the Quadratic Drag Model because this model's result is more accurate than a simpler one according to what I have read. $CD = CD_{min} + k * C_{L}^2$

That is my duty; Start the calculation with the aircraft at an altitude of 20,000 ft. and a full tank of fuel and finish the calculation when there are 100 litres of fuel remaining. For both the (a) range and (b) endurance analysis, provide separate results in cases when (i) the velocity [TAS] is kept constant and (ii) the altitude is kept constant. In all cases, the angle of attack should be kept constant. During this analysis, you can use the cruise SFC value.

And well, I couldn't start the step-by-step calculations in a regular sequence. I am hoping that someone can or will help me to determine proper sequence.


def calculator_atmosphere_values(h):
    # S-L reference values

    rho0 = 0.002378  # slugs/ft^3
    P0 = 2116  # psf
    T0 = 518.67  # R

    #############################
    Temperature_Ratio = (1 - 0.0000068756 * h)  # k values lapse  rate constant = 0.0000068756 / ft
    Pressure_Ratio = (1 - 0.0000068756 * h) ** 5.2561
    Densitiy_Ratio = (1 - 0.0000068756 * h) ** 4.2561

    #############################

    T_uk = Temperature_Ratio * T0 # R
    P_uk = Pressure_Ratio * P0 # psf
    rho_uk = Densitiy_Ratio * rho0 # slughs/ft^3

    ####################################################

    rho = rho_uk * 515.378818 # converting to kg/m3
    T = T_uk / 1.8 # converting to Kelvin
    P = P_uk * 47.88 # converting to Pascal

    ####################################################

    print("################### Temperature  according to Height ######################")
    print(f"Temperature at {h} Altitude: {T} K")
    print("################### Atmospheric Pressure for Altitudes below 36.089 ft ######################")
    print(f"Pressure at {h} Altitude: {P} Pa")
    print("################### Atmospheric density according to Height ")
    print(f"Density at {h} Altitude : {rho} kg/m3")


    return T, P, rho, T_uk
```
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  • 1
    $\begingroup$ "my problem is determine Vcruise" what do you mean? $V_{cruise}$ is the speed at which you want to cruise, it's a given parameter not one that you calculate. Maybe you want to calculate maximum speed? Or speed for best endurance? Or speed for best loiter? Or stall speed?... $\endgroup$
    – sophit
    Commented Sep 28, 2023 at 15:02
  • $\begingroup$ Hi Bugra, welcome to aviation.stackexchange.com. I started to convert your parameters to MathJax for better readability. Please check if I made any mistakes and correct them if needed. $\endgroup$
    – DeltaLima
    Commented Sep 28, 2023 at 15:19
  • $\begingroup$ Can you show what you have done so far? What are you trying to achieve at cruise speed? Maximum range or maximum endurance? $\endgroup$
    – DeltaLima
    Commented Sep 28, 2023 at 15:22
  • $\begingroup$ yes exactly what i want calculate Max range and Max endurance constant altitude and speed , I have done calculate pressure, temperature and density at 20.000 ft by using Temperature_Ratio = (1 - 0.0000068756 * h) # k values lapse rate constant = 0.0000068756 / ft Pressure_Ratio = (1 - 0.0000068756 * h) ** 5.2561 Densitiy_Ratio = (1 - 0.0000068756 * h) ** 4.2561 these equation. I also calculated CL = CL0 + alpha * CLa i have alpha at stall so that I calculated CLmax and Vstall and after i calculated Thrust value T = (P * (746 / 1000) / 0.2) * np # Newton at Cruise $\endgroup$
    – Bugra
    Commented Sep 28, 2023 at 16:09
  • 1
    $\begingroup$ @Bugra you would be better to edit the detail into your question. If you have a look at the syntax for mathjax, it will make it much more readable. $\endgroup$
    – Jamiec
    Commented Sep 28, 2023 at 16:27

1 Answer 1

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This is sort of a "do my homework" request, but it may be helpful to realize holding a constant angle of attack will mean a faster airspeed with a full tank and a slower airspeed with 100 liters remaining.

You may then use your drag coefficient and airspeed data to calculate thrust requirement, then determine fuel consumption rate to provide that thrust from the time the fuel tank is full to the time it contains 100 liters.

The lift requirement decreases by the weight of the fuel burned.

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  • $\begingroup$ Indeed, this is a prompt to set up a variety of integrals and see how their results differ. The 'constant alpha' and simple drag polar will mean that flight occurs at constant CL, which means constant CD and constant L/D. Since W will vary, D will vary, but in simple terms, the integral can be written in terms of weight. Then things start to go off the rails... They're told to work the problem in two forms - one constant TAS, the other constant altitude. In both cases, power required will change - and are unlikely to ever equal the specified cruise power. But, eta and SFC are constant. $\endgroup$ Commented Sep 29, 2023 at 0:08
  • $\begingroup$ @RobMcDonald this is where common sense takes over. Gliders commonly vary their Vbg based on weight. Optimal wing AoA is critical. I'd look into the Breguet equation. $\endgroup$ Commented Sep 29, 2023 at 9:25
  • $\begingroup$ well, I selected CLminD so that I got CD = CDmin after than I calculated Vcruise speed by using T = D equation then calculated TAS, CAS, EAS and then I am goin to using TAS to finding R according to the Breguet equation constant velocity and altitude conditions. Am i going right? $\endgroup$
    – Bugra
    Commented Sep 29, 2023 at 13:31
  • $\begingroup$ @Bugra yes. I would do min fuel consumption first, then go have a talk with whoever gave the assignment. $\endgroup$ Commented Sep 29, 2023 at 16:35
  • $\begingroup$ @bugra You can't set CD=CDmin. Although the name makes you think that is possible, that would be a condition for zero lift -- perhaps flying a parabolic arc, but that is not a condition for T=D and L=W. $\endgroup$ Commented Sep 29, 2023 at 17:02

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