In watching an airplane take off from a short runway you ove

In watching an airplane take off from a short runway, you overhear someone say he is concerned about the length of the runway because the temperature is so high and the humidity so low. You are not quite sure why these factors should be a cause for concern, so you return to your office and calculate air density at 90°F and 20% relative humidity and at 80°F and 50% relative humidity. You then search the Internet and find that L=Cu2A, where L is lift (the upward force provided by air flowing over and under a wing), C is a coefficient that depends on wing characteristics, is the density of air, u is the velocity of air over the wing, and A is the wing area. Is the overheard concern justified? Explain your response.

Solution

Density decreases with increasing temperature and with lower humidity there is less water in the air and hence lower density so a higher temperature and lower humidity leads to a lower density than other days.

Lower density would lead to a lower lift. If the lift is too low then the aircraft can\'t balance his weight. We don\'t know by exactly how much the humidity is and the temperature to comment on how much the lift is reduced but aircrafts do have a factor of safety to take care of such cases and then there are flaps in the wings to add to the lift.

So there isn\'t anything to be concerned about most likely