Question

During landing, an airplane experiences a net vertical ground reaction of \(15{,}000\ \text{N}\). The weight of the airplane is \(10{,}000\ \text{N}\). The landing vertical load factor, defined as the ratio of inertial load to the weight of the aircraft, is __________ (rounded off to 1 decimal place).

Hint:

Be careful with the definition used: many texts define load factor as \(R/W\). Here it's explicitly "inertial load to weight," i.e., \((R-W)/W\). Always read the definition in the problem.

Answer 1

Step 1: Interpret "inertial load."
In landing, the ground reaction \(R\) exceeds the weight \(W\). The inertial load is the excess over weight that produces deceleration/acceleration, i.e. \[ L_{\text{inertial}} = R - W. \] 

Step 2: Compute inertial load and the defined factor.
Given \(R=15000\ \text{N}\), \(W=10000\ \text{N}\): \[ L_{\text{inertial}}=15000-10000=5000\ \text{N}. \] The landing vertical load factor (as defined) is \[ n=\frac{L_{\text{inertial}}}{W}=\frac{5000}{10000}=0.5. \] Rounded to one decimal place: \(\boxed{0.5}\).