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6 Answers

Interpolation

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Flight Instructor, Private Pilot

Question 3678 for the Private Pilot Written Test states

(refer to figure 36) which is a Cruise Power Settings Table

 

Approximately, what TAS should a pilot expect with 65% max continous power at 9,500 feet with a temp of  36 degrees F below Standard.  

8000  = 181 MPH for TAS

10000 = 184 MPH for TAS  

Answer is 183 MPH

My question is how is a good way to teach interpolation to my students that don't understand it? 

Kyle

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6 Answers

  1. Best Answer


    Wes Beard on Mar 05, 2011

    There are two ways that I typically teach it depending on if they have a mathematical mind or not.
     
    Mathematical Way
    1.  10,000ft – 8,000ft = 2000ft     getting a ratio of where the cruise altitude lies
    2.  9,500ft – 8,000ft = 1,500ft
    3.  1,500ft / 2,000ft = .75
    4.  184 KTAS – 181 KTAS = 3  KTAS      applying that ratio to the KTAS
    5.  3 KTAS * .75 = 2.25 KTAS
    6.  181 KTAS + 2.25 KTAS = 183.25 KTAS
     
    Non Mathematical Way
     Is 9500ft closer to 8000ft or 10000ft?  The final value must be closer to the speed at 10000ft.  How close depends on the difference between the speeds.  In this case only a single know loss will work and we come up with 183 KTAS.

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  2. Curtis Ide on Mar 05, 2011

    Wes has a good technique.  For the mathematical mind I can throw in some X’s and Y’s but I am only doing the same thing with plug-in mathmatical equation.  This is probably more confusing but you can plug any numbers into this.  You can change out X or Y for altitude/airspeed/fuel burn/etc…
    X1, X2, X3 = Altitudes
    Y1,Y2, Y3 = Airspeeds
    we know X1=8000 and X2=10000 and X3=9500
    we know Y1=181 and Y2=184 and Y3=Unknown
    Equation y3= ((x3-x1)(y2-y1)/(x2-x1))+y1
    AKA = y3 = ((9500-8000)(184-181)/(10000-8000))+181
    y3=((1500)(3)/2000))+181
    y3=(4500/2000)+181
    y3=2.25+181
    y3=183.25
     

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  3. Steve Pomroy on Mar 05, 2011

    Hi Kyle.
     
    The above techniques work fine.  But if you have a math-phobic student who is very visual, you might want to try graphing the problem.  This approach works nicely on the ground, but not so nicely in the airplane.  But it helps to build understanding so that the techniques above can become more intuitive.  Try the following graph for the listed problem:

     

     
    Cheers,
    Steve
    http://www.flightwriter.com

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  4. Steve Pomroy on Mar 05, 2011

    Hmmm… Not sure why the image didn’t display.

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  5. Brett Gann on May 03, 2011

    I am studying for my private pilots test and the only thing i am having issues with is interpolation, i am fine at doing math but what i have issued with is figuring what to add, subtract, divide, and/or multiply. Is there some standard equation i can use or does it change with every situation?
     
    Brett Gann

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  6. nreim1 on May 06, 2016

    I have been working on my LSA and when planning my flights I really screw up interpolating the winds aloft. I can do simple math and some algebraic equations, but I don\’t always know what I need to be adding, subtracting, dividing or multiplying. If I wanted to find how much the wind is changing either faster or slower what am I suppose to do? I get that for WAF we gets data for the following altitudes
    3000ft 6000ft. 9000ft
    3221 3321+03 2916-03
    320@21 330@21 290@16. I am flying at 4500ft and 7500ft how do I properly interpolate this? I need the exact(or close) wind velocity at my planned altitudes.

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