| A
i r c r a f t S u p e r C a l c u l a t o r 6
. 1
(Mean Aerodynamic Chord, Neutral Point, Center
of Gravity, and Weight & Balance)
|
| MAC
And Neutral Point
If
no changes are seen in results after updating an input field,
then click BOTH compute/refresh buttons. |
use
the same units of measure (inches or feet) for all entries!
Center
of Gravity (CG) is the point where the WEIGHT of the aircraft
is balanced. Neutral Point (NP) is the point where the
AERODYNAMIC FORCES generated by the wing and tail are balanced.
Placing
CG 5% - 15% of MAC in front of NP creates a longitudinal (pitch)
stability called Static Margin. A lower margin produces
less stability and greater elevator authority, while a higher
margin creates more stability and less elevator authority. Too
much static margin results in elevator stall at take off and
landing.
25% - 35% MAC is generally accepted as a good range for
the CG of a conventional tailed aircraft where the AC of the
wing is at 25% MAC.
|
The Equations
|
Wing
Sweep, C = |
(S * (A + 2B))
/ (3 * (A + B)) |
| MAC
(length) = |
A - (2 * (A -
B) * (0.5 * A + B) / (3 * (A + B))) |
| MAC
location, d = |
Y * ((A - MAC)
/ (A - B)) |
| wing
area, WA = |
Y * (A + B) |
| tail
area, TA = |
YY * (AA + BB) |
| wing
aspect ratio, ARw = |
((Y * 2) ^ 2)
/ WA |
| tail
aspect ratio, ARt = |
((YY * 2) ^ 2)
/ TA |
| Tail
Arm = |
(D - wing
AC) + tail AC |
| tail
volume, Vbar = |
(TA / WA) * (Tail
Arm / MAC) |
| NP
(%MAC) = |
0.25 + (0.25
* sqr(sqr(ARw)) * Vbar |
| ideal
CG (%MAC) = |
NP - Desired
Static Margin |
| Moment
(total) = |
(Lt wheel Wt
* Lt Arm) + (Rt Wheel Wt * Rt Arm) + (Center Wheel Wt * Center Arm)
+ (Pilot Wt * Pilot Arm) + ( Psngr Wt * Psngr Arm) + (Fuel Wt * Fuel
Arm) |
| actual
CG (%MAC) = |
((Moment / Total
Wt) - (Datum2LE + C)) / MAC |
| actual
static margin % = |
(NP - actual
CG) / MAC * 100 |
NOTE:
This calculator can be distributed by permission only simply
by copying the contents between the first and last <table>
tags. Javascript equations and functions are fully contained
within it. DO NOT REPURPOSE BY EDITING any html or javascript
contained herein without permission.
email Dean A. Scott at dascott / at / southern
/ dot / edu to obtain distribution clearance and repurposing/reuse
permission.
CG
/ MAC Calculator adapted from the Public Domain. Neutral Point
and Weight & Balance Calculators developed by Dean A. Scott
(c) 2005, all rights reserved. Use with permission.
NP equations courtesy
Alasdair Sutherland (see
C.G. Position article on
Bloobird Radio Flyers)
|
|
Enter the following
data:
|
Wing |
Tail |
| Root
Chord (A, AA) : |
|
|
|
Tip Chord (B, BB) : |
|
|
|
Sweep Distance (S, SS) : |
|
|
|
Half Span (Y, YY) : |
|
|
| Distance
between wing & tail root LE's (D) : |
|
| Desired
Static Margin
(5% = twitchy 20% = mushy 10% - 15% recommended)
: |
|
|
|
| Weight
And Balance
|
| |
Weight |
Arm |
| Left
Main Wheel : |
|
|
| Right
Main Wheel : |
|
|
| Nose
or Tail Wheel : |
|
|
| Pilot
: |
|
|
| Passenger
: |
|
|
| Fuel
Tank (gallons of gas) : |
|
|
|
| Datum
Point from Wing Root LE : |
|
| Wing
Root Chord (A) : |
|
| Sweep
length at MAC : |
|
| MAC
length : |
|
| For
more accurate results, enter the values for Sweep Length and MAC
computed from the "MAC and NP" calculator above (shown below
in yellow).
|
Calculated
Results |
|
Mean Aerodynamic Chord (MAC) = |
|
|
MAC distance from root chord (d) = |
|
| Wing
Aerodynamic Center aft of root LE = |
|
|
Ideal Center of Gravity %MAC = |
|
| Actual
Center of Gravity %MAC = |
|
| Ideal
CG aft of root LE = |
|
| Actual
CG aft of root LE = |
|
| Actual
CG from main axle (neg. is aft) = |
|
|
Neutral Point %MAC (NP) = |
|
|
Neutral Point aft of Wing's root LE (NP) = |
|
|
Distance between Ideal CG and NP (E) = |
|
| Distance
between Actual CG and NP = |
|
|
Desired Static Margin % = |
|
|
Actual Static Margin % = |
|
|
Gross Takeoff Weight of Aircraft = |
|
|
Empty Weight of Aircraft = |
|
| |
Wing
Area = |
|
Tail
Area = |
|
Wing
Apsect = |
|
Tail
Aspect = |
|
| Wing
Taper = |
|
Tail
Taper = |
|
| W
sweep C = |
|
T
sweep CC = |
|
| Tail
MAC = |
|
T
MAC dist = |
|
| Tail
Arm = |
|
Vbar
= |
|
| Lt
wheel mnt = |
|
Rt
wheel mnt = |
|
| Center
wheel mnt = |
|
Pilot
mnt = |
|
| Passngr
mnt = |
|
Tank
mnt = |
|
| |
|
|
|
| |
|
|
|