Breguet Range Model

[mjburton11]

Hey we should have a Breguet Range Model. Woody and I discussed that there are multiple versions of the Breguet Range such as when it applies to props and when it applies to jets. I'm going to make a very simple model that we can then build off of.

[whoburg]

Here's one source for some of the versions: Range: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node98.html Endurance: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node99.html

I have a hunch that one way to start unifying is to have all Breguet models predict time, not range, and then range is just V*t. But there are still a number of different modeling assumptions that need to be supported -- BSFC constant, TSFC constant, etc.

[mjburton11]

Had some problems with the Breguet Range equation. I know I'm to supposed to post a lot of code but, I wasn't sure how to deal with this. These are the issues I'm having:

1) Don't no how to bound my initial and final weights.
2) I'm not sure how to put an upper bound on LoverD without going to into a lot of Drag calculations. But maybe that's what I want to do.

3) Not sure how to deal with TSFC at this point so I just bounded it with a number, which is probably not the best way to go about that.

# Constants
g = Variable('g', value=9.8, units='m/s^2')
a0 = Variable('a_0', value=340.29, units='m/s', label="speed of sound at sea level")
TSFC_min = Variable('TSFC_{min}', value=0.307, units='lb/lbf/hr', 
                    label="Minimum TSFC value")
M_min = Variable('M_{min}', value=0.6, label="Minimum Mach number")
MTOW = Variable('MTOW', value=10000, units='lbf', label="Max Take off Weight")
t_min = Variable('t_{min}', value=3, units='hr', label='Minimum Flight Time')

# Free Variables
R = Variable('R', units='nautical_miles', label="range")
M = Variable('M', label="Mach number")
LoverD = Variable('L/D', label="lift to drag ratio") 
TSFC = Variable('TSFC', units='lb/lbf/hr', label="thrust specific fuel consumption")
W_init = Variable('W_{init}', units='lbf', label="Initial Weight")
W_end  = Variable('W_{end}', units='lbf', label="Final Weight")
W_fuel = Variable('W_fuel', units='lbf', label="Fuel Weight")
z_bre = Variable('z_{bre}', label="Breguet parameter")
t = Variable('t', units='s', label='Time')

t = R/M/a0

models = [W_init >= W_end + W_fuel,
          W_init <= MTOW,
          LoverD >= 1,
          TSFC >= TSFC_min,
          M >= M_min,
          z_bre >= t*TSFC*g/LoverD,
          t >= t_min,
          W_init/W_end >= te_exp_minus1(z_bre, nterm=3),
         ]

return Model(1/R, models)

[whoburg]

@mjburton11, did we resolve some of this in person today?

[mjburton11]

Yes we did. Thanks!

[mjburton11]

@whoburg, Hey I was trying to run this Breguet Range model. I have defined free variables, constraint and objective functions I just did not include them here.

        def setup(self, TSFC_min=0.307, MTOW=10000, W_oew=7000, LoverD_max=15, M_max=0.78):
                #store attributes for later external use
                self.TSFC_min, self.MTOW, self.W_oew, self.LoverD_max, self.M_max = TSFC_min, MTOW, W_oew, LoverD_max, M_max
                TSFC_min = Var('TSFC_{min}', TSFC_min, "lb/lbf/hr")
                MTOW = Var('MTOW', MTOW, "lbf")
                W_oew = Var('W_{oew}', W_oew, "lbf")
                LoverD_max = Var('LoverD_{max}', LoverD_max)
                M_max = Var('M_max', M_max)
 ...

if __name__ == "__main__":
        m = Breguet_Range(0.307, 10000, 7000, 15, 0.78)
        sol = m.solve()

And I got this error:

File "breguet_range.py", line 59, in <module>
    m = Breguet_Range(0.307, 10000, 7000, 15, 0.78)
  File "/Users/mjburton11/.local/lib/python2.7/site-packages/gpkit/model.py", line 93, in __init__
    self.constraints = list(constraints)
TypeError: 'int' object is not iterable

Do you know why this is happening?

[bqpd]

If you send me the whole code, I can figure it out.

[mjburton11]

from gpkit.shortcuts import *

class  Breguet_Range(Model):

        """Breguet Range Model

        Arguments
        --------------------
        TSFC_min 
                Minimum TSFC value, assumed constant
        MTOW 
                Max Take Off Weight
        W_oew 
                Operating empty weight
        LoverD_max
                Maximum Lift to Drag ratio
        M_max
                Maximum Mach number 

        """
        def setup(self, TSFC_min=0.307, MTOW=10000, W_oew=7000, LoverD_max=15, M_max=0.78):
                #store attributes for later external use
                self.TSFC_min, self.MTOW, self.W_oew, self.LoverD_max, self.M_max = TSFC_min, MTOW, W_oew, LoverD_max, M_max
                TSFC_min = Var('TSFC_{min}', TSFC_min, "lb/lbf/hr")
                MTOW = Var('MTOW', MTOW, "lbf")
                W_oew = Var('W_{oew}', W_oew, "lbf")
                LoverD_max = Var('LoverD_{max}', LoverD_max)
                M_max = Var('M_max', M_max)

                #Constants
                g = Var('g', 9.81, "m/s^2","gravity")
                a0 = Var('a0', 340.29, "m/s", "speed of sound at sea level")

                #Free Variables
                R = Var('R', "nautical_miles", "range")
                M = Var('M', "Mach number")
                LoverD = Var('LoverD', "life to drag ratio")
                TSFC = Var('TSFC', "lb/lbf/hr", "thrust specific fuel consuption")
                W_init = Var('W_init', "lbf", "initial weight")
                W_fuel = Var('W_fuel', "lbf", "fuel weight")
                z_bre = Var('z_{bre}', "Breguet parameter")
                t = Var('t', "hr", "time")

                #Set up Model Equations
                objective = 1/t #Maximize time
                constraints = [
                                W_init >= W_oew + W_fuel,
                                W_init <= MTOW,
                                LoverD <= LoverD_max,
                                TSFC >= TSFC_min,
                                M <= M_max,
                                t <= T/M/a0,
                                z_bre >= t*TSFC*g/LoverD,
                                W_fuel/W_end >= te_exp_minus1(z_bre, nterm=3)
                                ]
                return objective, constraints

if __name__ == "__main__":
        m = Breguet_Range(0.307, 10000, 7000, 15, 0.78)
        sol = m.solve()

[bqpd]

(oh, shoot, sorry, missed that this was also a PR & branch with the code already)

[mjburton11]

This was resolved a while ago so I'm going to close it.

[whoburg]

:+1: