Welcome Guest. Sign in or Signup

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? 


Ace Any FAA Written Test!
Dauntless Aviation's GroundSchool series of apps are the smart pilot's choice for fast and effective FAA knowledge test prep.
Actual, up-to-date FAA questions Polished user experience
Best explanations in the business Free lifetime updates!
Private Pilot IFR Commercial Pilot CFI ATP Sport Pilot Sport Pilot Instructor Parachute Rigger Aviation Mechanic (A&P)
You can get the app now and be studying right away. Available for PC, Mac, iPhone/iPad, and Android.

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.

    +6 Votes Thumb up 6 Votes Thumb down 0 Votes

  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

    +2 Votes Thumb up 2 Votes Thumb down 0 Votes

  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:



    +1 Votes Thumb up 1 Votes Thumb down 0 Votes

  4. Steve Pomroy on Mar 05, 2011

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

    0 Votes Thumb up 0 Votes Thumb down 0 Votes

  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

    0 Votes Thumb up 0 Votes Thumb down 0 Votes

  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.

    0 Votes Thumb up 0 Votes Thumb down 0 Votes

The following terms have been auto-detected the question above and any answers or discussion provided. Click on a term to see its definition from the Dauntless Aviation JargonBuster Glossary.

Answer Question

Our sincere thanks to all who contribute constructively to this forum in answering flight training questions. If you are a flight instructor or represent a flight school / FBO offering flight instruction, you are welcome to include links to your site and related contact information as it pertains to offering local flight instruction in a specific geographic area. Additionally, direct links to FAA and related official government sources of information are welcome. However we thank you for your understanding that links to other sites or text that may be construed as explicit or implicit advertising of other business, sites, or goods/services are not permitted even if such links nominally are relevant to the question asked.