Class I weight estimation: Theory: An iteration method is used to estimate the airplane take-off weight. The iteration starts with a guessed value of take-off weight (defined by users). The guessed take-off weight is used to solve for the airplane empty weight with the two equations shown below: log10 WE
log 10 WTO A B
Eqn. (1)
A & B Coefficient: A= 0.6632 (Single Engine Military Trainer) B=0.8640 (Single Engine Military Trainer) This equation represents a linear relationship between the logarithm of the airplane empty weight and the logarithm of the airplane take-off weight for airplanes of same type. The line that represents the relationship is called the Regression line. The take-off weight regression coefficients, A and B, for different types of airplane are listed in (1) 1; they can also be determined using regression techniques:
WE 1 1 M ff 1 M Fres M tfo WTO WPL WCrew WPLexp WFrefuel n
M ff M ff i i 1
1 WTO
n 1 WPLexpi 1 i 1
1 M ff i j i 1 WTO n
n 1 WFrefuel 1 i 1
Eqn. (2)
M ff j j i 1 n
where : Wi WFusedi M ff i Wi n
WPLexp WPLexp i 1
i
n
WFrefuel WFrefueli i 1
The airplane empty weights calculated from the two equations are compared. If the following condition is satisfied, the guessed take-off weight will be accepted as the take-off weight for this particular airplane. If the condition is not satisfied, the program would adjust the guessed takeoff weight and repeat the calculation until the condition is satisfied: W E ( Eqn.2) W E ( Eqn.1) 0.05lbs
Eqn. (3)
Once the take-off weight is determined, the weight of the fuel used in the mission is estimated from:
WFused (1 M ff )WTO 1
Eqn. (4)
Roskam J., Airplain Design Part I; 1999 Section 2.7.1, P. 69
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