Calculating MAC% for the Stinson 108-3

WARNING: This is an experimental application and is not to be used for flight planning purposes.

First we define the Stinson 108 - 3 CG Envelope per the diagram in the POH

envelope[x_] := 0 /; x < 18.2;
envelope[x_] := 2400 /; x ≥ 28.8 && x ≤ 38.5;
envelope[x_] := 1750 + (x-18.2)(650/10.6)  /; x ≥ 18.2 && x < 28.8;

MAC% as defined in the POH for Stinson 108-3. The products of the weights and their arms are totaled and divided by the total weight and 0.52 is subtracted from the ratio. This result is divided by 55.5% to arrive at percent MAC.

mac[weight_,station_] := ((((Total[weight station])/(Total[weight])))-.52)/.555

In the following panel you may explore the effect that changing various weights and arms has on the CG. The first five weight settings are for aircraft empty weight, fuel, front seat weight, rear seat weight, and cargo area respectively. The next three weight settings are for additional entries at stations other than the front or rear seats or cargo area. The first five station entries are for the empty weight CG, fuel station, front seat station, rear seat station, and cargo station respectively. The last three stations are for the last three weight stations.

As the weights and stations are adjusted the calculated MAC% is plotted as a point on the graph.

Manipulate[Plot[{envelope[x]},{x,16,40},Filling->Bottom,PlotRange->{{16,40},{0,2500}},AxesOrigin->{17,0},Epilog->{Point[{mac[{ew,fuel,front,rear,cargo,w1,w2,w3},{ewcg,fuelStation,frontStation,rearStation,cargoStation,station1,station2,station3}],Total[{ew,fuel,front,rear,cargo,w1,w2,w3}]}]}],{{ew,1325,"Empty Wt"},1100,1500,10,Appearance->"Labeled"},{{fuel,300,"Fuel Wt"},0,324,1,Appearance->"Labeled"},{{front,150,"Front Wt"},75,600,5,Appearance->"Labeled"},{{rear,0,"Rear Wt"},0,600,5,Appearance->"Labeled"},{{cargo,0,"Cargo Wt"},0,100,1,Appearance->"Labeled"},{{w1,0,"Weight 1"},0,500,1,Appearance->"Labeled"},{{w2,0,"Weight 2"},0,500,1,Appearance->"Labeled"},{{w3,0,"Weight 3"},0,500,1,Appearance->"Labeled"},{{ewcg,12.5,"Empty Wt CG"},10,15,.01,Appearance->"Labeled"},{{fuelStation,6,"Fuel Station"},0,30,.01,Appearance->"Labeled"},{{frontStation,20,"Front Seat Station"},10,25,1,Appearance->"Labeled"},{{rearStation,56,"Rear Seat Station"},45,60,1,Appearance->"Labeled"},{{cargoStation,78,"Cargo Station"},60,90,1,Appearance->"Labeled"},{{station1,0,"Station 1"},-100,500,1,Appearance->"Labeled"},{{station2,0,"Station 2"},-100,500,1,Appearance->"Labeled"},{{station3,0,"Station 3"},-100,500,1,Appearance->"Labeled"},SaveDefinitions->True]

Copyright © 2009 Jim Michael
Please email comments and corrections to jm@10squaredcorp.com