Question

Aeroplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. The indicated airspeed is the airspeed given by an instrument called an airspeed indicator. A plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. The true airspeed is the speed of the aeroplane relative to the wind. Ground speed is the speed of the aeroplane relative to the ground. For example, a plane flying at a true airspeed of 150 knots with a headwind of 25 knots will have a ground speed of 125 knots.

The problems below refer to static and dynamic pressure. Static pressure is used when a body is in motion or at rest at a constant speed and direction. Dynamic pressure is used when a body in motion changes speed, direction, or both. A gauge compares these pressures, giving pilots an indication of airspeed.
In problems 1 and 2, use the following information:
The indicated airspeed S (in knots) of an aeroplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures.
The relationship between S and p can be modeled by S=136.4p−−√+4.5.
1. Find the differential pressure when the indicated airspeed is 157 knots.
2. Find the change in the differential pressure of an aeroplane that was travelling at 218 knots and slowed down to 195 knots.
In problems 3 and 4, use the following information:
The true airspeed T (in knots) of an airplane can be modeled by T=(1+A50,000) ⋅ S, where A is the altitude (in feet) and S is the indicated airspeed (in knots).
3. Write the equation for true airspeed T in terms of altitude and differential pressure p.
4. A plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet.
Estimate the differential pressure. Explain why you think your estimate is correct.

Answer 1

The differential pressure for indicated airspeeds and the true airspeed in terms of altitude and pressure can be calculated using the provided equations, allowing one to estimate changes in airspeed and the required heading adjustments for different wind conditions and altitudes.

Step-by-step explanation:

To address the questions concerning airplane speeds and their measurement, we can use the given models and formulas.

Question 1:

To find the differential pressure when the indicated airspeed is 157 knots, we use the formula S=136.4√p+4.5. We solve for p by plugging in S = 157 and isolating p.

Question 2:

To find the change in the differential pressure as the airplane slows down from 218 knots to 195 knots, we calculate the differential pressure for both airspeeds using the provided formula and then find the difference.

Question 3:

For the true airspeed T equation in terms of altitude A and differential pressure p, we combine the two given formulas to get T = (1+A/50,000) × (136.4√p + 4.5).

Question 4:

Given a true airspeed of 280 knots and an altitude of 20,000 feet, we can estimate the differential pressure by inputting these values into the combined equation from Question 3 and solving for p.