I occasionally get questions in my inbox and I feel like some of them would be useful to post publicly. I will try to do so in the future.
EVERYTHING described at ISA SL unless otherwise stated.
Hello Keith,
Coefficients are used anytime the data being analyzed is bound to a set of mathematical rules by it's relationship with physics. The drag coefficient is not dynamic, but the physical atmosphere is.
So let's take CD0: If a conventional airplane in level flight at mach 0.2 creates 2000 pounds of drag, and we have subtracted 500 pounds of ram drag and 500 pounds of lift drag, leaving 1000 pounds of drag, that remaining balance must be parasitic drag (CD0)---because we are so slow there is no useful mach drag to worry about...
at sea level mach 0.2 the airplane is moving at a Dynamic q of 59.256 [q = 1481.4*mach^2 * pressure ratio "Delta"]. ("q" or "dynamic pressure", indicates the mass flow rate of air the wing can influence per second in a non-dimensional number.)
so we simply divide our drag into q * S "Wing Area" to get the coefficient. Assuming a wing area of 1000... 1000 / ( 59.256*1000 ) = 0.0168759 drag coefficient.
and so now we know, if this airplane flies at any weight and speed we can simply multiply S * q * drag coefficient --- because q will scale the drag pounds up or down with changes of speed or altitude.
So it is important to understand that q works in 1 dimension. 59 q at FL350 will produce the same amount of drag as 59 q at SL, scaled appropriately to density effects.
Alright, now that we got that out the way, it sounds like you are on the right track. I'm assuming you are using multiple lines on the thrust table and not using the ram drag table (recommended).... If so, find the cruise charts for the airplane.
Equations are at the bottom.
First, we need to figure ram drag using the fuel flow efficiency on the cruise charts;
step 1a) convert the real airplane's N1 to CN1, then convert the fuel flow to Corrected FF; note the Mach.
What we are attempting to do in this step is convert our ambient engine to a SL condition that we can use as a reference.
step 2a) find your engine's fuel flow for that CN1 on your static fuel flow chart (you can easily make that by multiplying static thrust * static SFC; check video of taxi N1/FF at sea level)
This is simply static SL fuel flow at that CN1.
step 3a) compare the static SL fuel flow and the corrected fuel flow number; The CFF number should be higher meaning less efficient (burned more fuel at the same fan speed) Find the CN1 where the CFF and static FF are equal and record that Static Thrust number.
We are doing two things here: 1) Comparing static sea level FF to mach 0.X SL FF.....so speed affect on fuel flow at sea level; 2) Finding how much STATIC thrust it would take to equal the high speed FF.
The difference between static thrust and the CFF Thrust number is thrust loss due ram drag. Record that as a SEA LEVEL Ram drag data point for that mach..... restart for a different mach. I usually do even 20s. 0.2 0.4 0.6 0.8 and any areas where there is a large curvature in the thrust chart.
What we are doing in this step is taking the difference in thrust to determine efficiency loss. We don't really care why (unless we are designing the engine or areas to attach), all we care is that loss is not based on lift, mach, or form. Lump what's there into SL ram drag.
Enter all this data into the thrust table.......and chart it graphically for inspection and cross checking..
Next, we need to convert the SL thrust at CN1 up to the altitudes and mach of the original fuel flow plot.... then we can find drag required. Once we have drag required we subtract ram drag to find CD0 +mach drag
step 1b) look at all your plot points from above. Find SL thrust from step 3a, then convert thrust up to charted ambient conditions. This is gross thrust at that altitude. Convert you're derived ram drag up using the exact formula that you just used to convert the thrust. Subtract ram drag from gross thrust to find net thrust. This is total drag required. Use this for your flight test later to check your engine performance and use this in the next step.
step 2b) use the drag formula to derive the coefficient of drag required. redo for all mach points.
step 3b) enter your findings into a mach drag table, and look for the rise. everything below the rise is CD0, everything above is Mach rise. You can either shave the rise off and make the two entries or you can leave it in the mach drag table and set CD0 to 0. This is my preferred method in the sim. If you separate the two, remember that the mach rise is an additive and the two will be summed.
*
****
********** <--- mach rise additive
*********************** <--- CDo base
***********************
.0 .2 .4 .6 .8 <mach
Equations:
(ambient means cockpit gauge readout..i.e..what is charted)
Theta = Temperature ratio = Ambient temperature Celsius +273.15 / 288.15
Delta = Pressure ratio = ( [ 288.15 - (0.0019812 * Altitude Feet) ] / 288.15 ) to the power of 5.25588
step 1a) convert the real airplane's N1 to CN1: Ambient N1 / Theta^0.5 * (1 + (0.2*Mach)^2 )^3.5 = corrected N1
step 3a) find corrected fuel flow CFF: Ambient fuel flow / Delta * Theta * (1 + (0.2*Mach)^2 )^(3.5+0.5) = corrected fuel flow
step 1b) Convert SL thrust to Ambient altitude: Thrust pounds * Delta * (1 + (0.2*Mach)^2 )^3.5 = Ambient Thrust pounds
step 2b) convert drag to a coefficient: CD = drag pounds / q * S; q = 1481.4*mach^2 * Delta; S = airplane reference wing area.
All that is left is to convert to the 2048 integers of the airfile! It is a long process, and you will get confused and make mistakes; check your work frequently, and think through the physical rules.
A) engines perform the same under all conditions and altitudes, but mathematically, altitude scales thrust (total delta), and speed affects ram drag (intake momentum) and ram rise (total theta).
The thinner air affects fuel flow only because the optimum mixture is maintained from sea level as rule A scales the numbers.
B) non-lift drag would be the same at all altitudes and speeds (scaled by q*S) if it weren't from mach drag rise.... ( [CD*q*S] + mach drag rise)
C) An FS rule, fuel flow should be too low at higher speed due to a bug that derives fuel flow from NET thrust instead of gross thrust. You can use a fuel dump gauge to burn fuel from gross thrust.
D) Another FS rule, do not use CL versus mach lift at all during designing; thus your pitch will be way too high at high mach. FS fails to render compression effect on AoA, and so that stupid table is useless. If used it will reduce your induced drag excessively at high mach. Once the FDE is done, you can either add the lift back and tweak CDi + mach drag to compensate or you can make a gauge that lies about pitch inverse with the lift vs mach table you were going to use.
okay, I hope that is everything. Let me know if you have questions or get stumped. good luck!!!
EVERYTHING described at ISA SL unless otherwise stated.
Hello Keith,
Coefficients are used anytime the data being analyzed is bound to a set of mathematical rules by it's relationship with physics. The drag coefficient is not dynamic, but the physical atmosphere is.
So let's take CD0: If a conventional airplane in level flight at mach 0.2 creates 2000 pounds of drag, and we have subtracted 500 pounds of ram drag and 500 pounds of lift drag, leaving 1000 pounds of drag, that remaining balance must be parasitic drag (CD0)---because we are so slow there is no useful mach drag to worry about...
at sea level mach 0.2 the airplane is moving at a Dynamic q of 59.256 [q = 1481.4*mach^2 * pressure ratio "Delta"]. ("q" or "dynamic pressure", indicates the mass flow rate of air the wing can influence per second in a non-dimensional number.)
so we simply divide our drag into q * S "Wing Area" to get the coefficient. Assuming a wing area of 1000... 1000 / ( 59.256*1000 ) = 0.0168759 drag coefficient.
and so now we know, if this airplane flies at any weight and speed we can simply multiply S * q * drag coefficient --- because q will scale the drag pounds up or down with changes of speed or altitude.
So it is important to understand that q works in 1 dimension. 59 q at FL350 will produce the same amount of drag as 59 q at SL, scaled appropriately to density effects.
Alright, now that we got that out the way, it sounds like you are on the right track. I'm assuming you are using multiple lines on the thrust table and not using the ram drag table (recommended).... If so, find the cruise charts for the airplane.
Equations are at the bottom.
First, we need to figure ram drag using the fuel flow efficiency on the cruise charts;
step 1a) convert the real airplane's N1 to CN1, then convert the fuel flow to Corrected FF; note the Mach.
What we are attempting to do in this step is convert our ambient engine to a SL condition that we can use as a reference.
step 2a) find your engine's fuel flow for that CN1 on your static fuel flow chart (you can easily make that by multiplying static thrust * static SFC; check video of taxi N1/FF at sea level)
This is simply static SL fuel flow at that CN1.
step 3a) compare the static SL fuel flow and the corrected fuel flow number; The CFF number should be higher meaning less efficient (burned more fuel at the same fan speed) Find the CN1 where the CFF and static FF are equal and record that Static Thrust number.
We are doing two things here: 1) Comparing static sea level FF to mach 0.X SL FF.....so speed affect on fuel flow at sea level; 2) Finding how much STATIC thrust it would take to equal the high speed FF.
The difference between static thrust and the CFF Thrust number is thrust loss due ram drag. Record that as a SEA LEVEL Ram drag data point for that mach..... restart for a different mach. I usually do even 20s. 0.2 0.4 0.6 0.8 and any areas where there is a large curvature in the thrust chart.
What we are doing in this step is taking the difference in thrust to determine efficiency loss. We don't really care why (unless we are designing the engine or areas to attach), all we care is that loss is not based on lift, mach, or form. Lump what's there into SL ram drag.
Enter all this data into the thrust table.......and chart it graphically for inspection and cross checking..
Next, we need to convert the SL thrust at CN1 up to the altitudes and mach of the original fuel flow plot.... then we can find drag required. Once we have drag required we subtract ram drag to find CD0 +mach drag
step 1b) look at all your plot points from above. Find SL thrust from step 3a, then convert thrust up to charted ambient conditions. This is gross thrust at that altitude. Convert you're derived ram drag up using the exact formula that you just used to convert the thrust. Subtract ram drag from gross thrust to find net thrust. This is total drag required. Use this for your flight test later to check your engine performance and use this in the next step.
step 2b) use the drag formula to derive the coefficient of drag required. redo for all mach points.
step 3b) enter your findings into a mach drag table, and look for the rise. everything below the rise is CD0, everything above is Mach rise. You can either shave the rise off and make the two entries or you can leave it in the mach drag table and set CD0 to 0. This is my preferred method in the sim. If you separate the two, remember that the mach rise is an additive and the two will be summed.
*
****
********** <--- mach rise additive
*********************** <--- CDo base
***********************
.0 .2 .4 .6 .8 <mach
Equations:
(ambient means cockpit gauge readout..i.e..what is charted)
Theta = Temperature ratio = Ambient temperature Celsius +273.15 / 288.15
Delta = Pressure ratio = ( [ 288.15 - (0.0019812 * Altitude Feet) ] / 288.15 ) to the power of 5.25588
step 1a) convert the real airplane's N1 to CN1: Ambient N1 / Theta^0.5 * (1 + (0.2*Mach)^2 )^3.5 = corrected N1
step 3a) find corrected fuel flow CFF: Ambient fuel flow / Delta * Theta * (1 + (0.2*Mach)^2 )^(3.5+0.5) = corrected fuel flow
step 1b) Convert SL thrust to Ambient altitude: Thrust pounds * Delta * (1 + (0.2*Mach)^2 )^3.5 = Ambient Thrust pounds
step 2b) convert drag to a coefficient: CD = drag pounds / q * S; q = 1481.4*mach^2 * Delta; S = airplane reference wing area.
All that is left is to convert to the 2048 integers of the airfile! It is a long process, and you will get confused and make mistakes; check your work frequently, and think through the physical rules.
A) engines perform the same under all conditions and altitudes, but mathematically, altitude scales thrust (total delta), and speed affects ram drag (intake momentum) and ram rise (total theta).
The thinner air affects fuel flow only because the optimum mixture is maintained from sea level as rule A scales the numbers.
B) non-lift drag would be the same at all altitudes and speeds (scaled by q*S) if it weren't from mach drag rise.... ( [CD*q*S] + mach drag rise)
C) An FS rule, fuel flow should be too low at higher speed due to a bug that derives fuel flow from NET thrust instead of gross thrust. You can use a fuel dump gauge to burn fuel from gross thrust.
D) Another FS rule, do not use CL versus mach lift at all during designing; thus your pitch will be way too high at high mach. FS fails to render compression effect on AoA, and so that stupid table is useless. If used it will reduce your induced drag excessively at high mach. Once the FDE is done, you can either add the lift back and tweak CDi + mach drag to compensate or you can make a gauge that lies about pitch inverse with the lift vs mach table you were going to use.
okay, I hope that is everything. Let me know if you have questions or get stumped. good luck!!!
