Tranquillus, Analysis Data Item Vol. 1

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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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