Question

A model of a helicopter rotor has four blades, each 2.60 m long from the central shaft to the bladetip. The model is rotated in a wind tunnel at 477 rev/min. What is the radial acceleration of theblade tip expressed as a multiple of g?Answer:Choose...Next page

Answer 1

The radial acceleration in terms of the frequency and the radius is given by:

$a_c=4\pi^2rf^2$

To use this formula we need to convert the frequency to revolution per second:

$477\frac{rev}{\min}\cdot\frac{1\text{ min}}{60\text{ s}}=7.95\text{ Hz}$

Plugging the values we have:

$\begin{gathered} a_c=4\pi^2(2.6)(7.95)^2 \\ a_c=6487.35 \end{gathered}$

hence the acceleration is 6487.35 m/s^2. To get the acceleration in terms of g we divide it by its value:

$\begin{gathered} a_c=\frac{6487.35}{9.8} \\ a_c=661.97 \end{gathered}$

This means that the acceleration is approximately 662 times the acceleration of gravity, that is:

$a_c=662g$