I need help with an airspeed problem. Please?

Question

Okay, pretty simple problem, but not seeing the explanation in the book so far. A plane travels 900 miles in 2 hours and 55 minutes with the tail wind. It comes back in 3 hours and 26 minutes against the wind. What is the speed of the plane in still air and what is the speed of the wind?

Answer 1

Ok, so this is a distance = rate * time question



the operative factor here is the fact that RATE is affected by wind. If you have a tailwind (with the wind), then you fly at the speed of the plane PLUS the wind. If you have a headwind (against the wind), then you fly at the speed of the plane MINUS the wind (ignoring aerodynamic factors, of course).



Distance is the same in this case (you fly there and back), so both are 900. You need both equations because you have two variables.



Let's call the speed of the plane "p" and the speed of the wind "w" - and let's calculate everything in terms of minutes (so that we don't have both hours and minutes)



r1 * t1 = r2 * t2 = 900

(p + w) * (2*60 + 55) = (p - w) * (3*60 + 26) = 900

(p + w) * 175 = (p - w) * 206 = 900

[I combined them for convenience, but they are actually separate equations]



1. (p+w)*175 = 900

p+w = 900/175



2. (p-w)*206 = 900

p-w = 900/206





p+w = 900/175

p-w = 900/206

(you can add the two equations now or subtract them from each other, and that will leave you with just one variable. I will add them here)



2p + w - w = 900/175 + 900/206

2p = about 9.512 miles per minute (what a terrible number..)

p = about 4.756 mi/min (to find in mi/hr, just multiply by 60)





to find w, just plug it back into either equation. w = about 1.081 mi/min



ok.. that was ugly.. i hope that helps though

Answer 2

it rather works the similar way as a deliver on a river. The airspeed is the cost of the plane with delight in to the body of air, in basic terms because of the very truth the boats interior the route of the water velocity is with delight in to the water. For this way of situation you'll write 2 equations in 2 variables, and then clean up via ability of substitution a = airspeed (mph) w = windspeed (mph) 2:fifty 4 = 2.9 hrs 348 = 2.9(a-w) and 348 = 2.0(a+w) 348/2.9 + w = a and 348/2 - a = w so 348/2 - 348/2.9 -w = w (348/2 -348/2.9)/2 = w 27 = w ( wind velocity is 27 mph) 348/2 - a = 27 174 - 27 = a 147 = a (airspeed is 147 mph)

Answer 3

True airspeed (TAS) of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.







Low-speed flight

True airspeed (TAS) can be calculated as a function of indicated airspeed (or equivalent airspeed) and air density:



where TAS is true airspeed



VI is indicated (or equivalent) airspeed

ρ0 is 1.225 kg/m3, the air density at sea level and 15 degrees Celsius

ρ is the density of the air in which the aircraft is flying



High-speed flight

TAS can be calculated as a function of Mach number and static air temperature:





Where

TAS = true airspeed

asl is the standard speed of sound at 15 °C (661.47 knots)

Ma is Mach number,

T is static air temperature in kelvins,

Tsl is standard sea level temperature (288.15 K)

Combining the above with the expression for Mach number under subsonic compresible flow gives an expression for TAS as a function of impact pressure (pitot tube), static pressure and static air temperature:





Where

qc is impact pressure

P is static pressure

Electronic Flight Instrument Systems (EFIS) contain an air data computer with inputs of impact pressure, static pressure and total air temperature. In order to compute TAS the air data computer must convert total air temperature to static air temperature. This is a function of Mach number:





Where

Tt = total air temperature

For manual calculation of TAS in knots where Mach number and static air temperature are known the expression may be simplified to:





remembering that temperature is in kelvins and TAS in knots.



In simple aircraft, without an air data computer or Machmeter, true airspeed can be calculated as a function of calibrated airspeed and local air density (or static air temperature and pressure altitude which determine density). Some airspeed indicators incorporate a slide rule mechanism to perform this calculation. Otherwise, it can be performed using this java applet or a device such as the E6B (a handheld circular slide rule).





















http://www.airrouting.com/content/TimeDistanceForm.aspx



http://www.csgnetwork.com/tasinfocalc.html