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%MAC calculation

G

guda

Messages
8
Country
france
Hello,

I’m looking for a way to calculate %MAC for an empty airplane (no payload and FUEL). I've read the Yves Guillaume's PDF "Flight Dynamics in Microsoft Flight Simulator" and tried this method:

I use TopCAT as a reference for %MAC value. For a 737-800, the known variables are:

Wing Root Chord (A) = 18.9 ft

Wing Area = 1 341 ²ft

Wing Span (Y) = 112.6 ft

Wing SWEEP (S) = 25°

Wing Pos Apex Lon (CG) = 12.8413 ft

My calculation:

1: TIP CHORD (B) = Wing Area / Wing Span x 2 = 4.92 ft

2: MAC LENGTH = A-(2*(A-B) * (0.5 * A+B) / ( 3 * (A+B))) = 13.23 ft

3: Distance MAC LE aft of wing apex = ( S * (A+2*B)) / (3 * (A+B )) = 5.03 ft

4: Lateral offset of MAC from Wing Center line = ( 2 * Y * (0,5*A + B)) / (3 * (A+B)) = 45.28 ft

Is it correct?

Here, I’m stuck because I don’t how to integrate the variable Wing Pos Apex Lon CG (2.8413 ft) and to convert to%MAC

Thank you for your help.

Dan
 
Your equation for TIP CHORD seems to be incorrect:
1: TIP CHORD (B) = (2*Area/Span) - RootChord = 1.8922 ft

2: MAC LENGTH = A-(2*(A-B) * (0.5 * A+B) / ( 3 * (A+B))) = 14.1043 ft

3: Distance MAC LE aft of wing apex = ( S * (A+2*B)) / (3 * (A+B )) = 10.8889 ft

.4: Lateral offset of MAC from Wing Center line = ( 2 * Y * (0,5*A + B)) / (3 * (A+B)) =21.1876 ft - NOT NEEDED
Click to expand...

The relationships are shown in the sketch.

Capture.JPG
 
Hello,

Roy, yes I've read this other thread before to post here. The main part of these calculation are based on this thread.

AirWrench or another software doent' give me the MAC length or reference_datum_position so I have to calculate them.

Regarding mgh asnwer, I did a mistake in my copy/paste (I forgot "-Rootchord") but the result takes into account this variable. In my side I found 4.92 ft:
TIP CHORD (B) = (Area / Span x 2) - RootChord =( 1 341 / 112.6 * 2 ) - 18.9 = 23.82 - 18.9 = 4.92 ft
Am I reading this wrong? How do you find 1.8922 ft?

Dan
 
Dan,
Your tip chord number is correct.
AirWrench gives MAC on the Dimensions and Balance pages, it gives most of the answers needed.
Reference_datum_position is in the Weight and Balance section of the aircraft.cfg and is also in the side view of the AirWrench Balance page.
One of the issues here is that the methods commonly used tend to assume a simple tapered wing, and the 737 like many others has a straight trailing edge section which screws up the simple calculations.
Roy
 
Your equation is
TIP CHORD (B) = (Area / Span x 2) - RootChord =( 1 341 / 112.6 * 2 ) - 18.9 = 23.82 - 18.9 = 4.92 ft
Click to expand...

The default FSX B737-800 .cfg gives:
[airplane_geometry]
wing_area = 1344.0 //Square feet
wing_span = 117.42 //Feet
wing_root_chord = 21.0 //Feet
...
wing_sweep = 27.2 //Degrees, wing leading edge
wing_pos_apex_lon = 6.96 //Feet, longitudinal distance from reference
Click to expand...

My equation is:
TIP CHORD (B) = (Area / Span x 2) - RootChord =( 1344 / 117.42 * 2 ) - 21.0 = 22.8922 - 21.0 = 1.8922 ft
Click to expand...

the change seems to be different data.

EDIT

The default FSX B737-800 .cfg also gives:
empty_weight_CG_position = -9, 0, 0 // (feet) longitudinal, lateral, vertical distance from specified datum
Click to expand...
 
Last edited:
http://www.b737.org.uk/techspecsngs.htm

This is a link to drawings of the 737-800
My comments about the trailing edge just prove I'm not up to speed on airliners. This version has a short straight trailing edge between the engines, and the leading edge sweep varies so the classic equations will not work for tip chord etc.
However, it does also show that the default FS dimensions for the -800 are not all correct.
Wingspan without winglets is 112 feet 7 inches, with winglets it is 117 feet 5 inches.
Wing basic root chord, from fuselage centerline where leading edges would meet, to the straight part of the trailing edge is 25 feet 10 inches
Wing basic area is 1341 sq ft
Wingtip chord is 4 feet 1.25 inches. When you think about it a tip chord of only 1.89 feet would look weird on a wing of this span and root chord.
Aspect Ratio is 9.45
Taper Ratio is 0.159
MAC is 12.99 feet
Dihedral is 6°
1/4 chord sweep is 25.02°, so leading edge sweep is probably 27.2.
The document does not give any CG data
Roy
 
Thank you for your inputs.

In my situation, I don't need winglets or more precision. B737 is only an example. I have to calculate an "estimate" %MAC for any airplane with only these known variables: the Wing Root Chord (A), Wing Area, Wing Span (Y), Wing SWEEP (S) and Wing Pos Apex Lon (CG).

When I read the other thread, I don't understand how LEMAC is calculated.
empty_weight_cg_position = -35.79 ft
wing_apex_pos_lon = -31.5 ft
MAC = 7.28 ft
LEMAC = 2.37 ft (from wing_apex_pos_lon)​

how do we find this value without open AirWrench?
 
Given:
Wing Root Chord, Wing Area, Wing Span, Wing SWEEP and Wing Pos Apex Lon, find CG as % MAC.
Method:
1. taper_ratio=(2*wing_area/wing_span-wing_root_chord)/wing_root_chord

2. MAC =2/3*wing_root_chord*(1+taper_ratio+taper_ratio^2)/(1+taper_ratio)

3. sweep_offset=(wing_span/6)*((1+2*taper_ratio)/(1+taper_ratio))* tan(wing_sweep)

4. CoG %MAC=(wing_pos_apex_lon-empty_weight_CG position_lon-sweep_offset)/MAC

This is the method I generally use
Roy
 
FSX itself internally calculates the Centre of Gravity based on the [WEIGHT_AND_BALANCE] and [fuel] sections in the .cfg file, and the dynamic Aircraft Fuel Data in the FSX variables.

FSUIPC offsets give:

0x2E78 CG percent laterally, as a double (FLOAT64). This is the position of the actual CoG as a fraction (%/100) of MAC (Mean Aerodynamic Chord)
0x2EF8 CG percent, as a double (FLOAT64). This is the position of the actual CoG as fraction (%/100) of MAC (Mean Aerodynamic Chord)

My calcuations shows that the CG percentages are based on the values in .cfg file and the Aircraft Fuel Data variables - including MAC and MAX_LE
 
Hello,

Thank you. I will work on it as soon as I come back in two keeks.

Thank you again for your help

Dan
 
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