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 =