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RoC/RoD and TAS v GS

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  • RoC/RoD and TAS v GS

    Morning Colin,

    I hope you and yours are keeping well and gainfully 'employed' on the golf courses and cruise ships of the world.

    Here's one for you, which I have just encountered and it is bugging me - surprised it's never come up before (or maybe it has and I have missed it). I'm sure there will be more than one student out there thinking the same.

    Why are RoC and RoD in Performance based on TAS, e.g. Gradient = ROC/TAS x 6000/6080, whereas in Gen and Radio Nav they are based on GS.

    As rate of climb/descent is based on a change of height over a ground distance covered, I would have thought that the correct formula would have been:

    Gradient = ROC/GS x 6000/6080

    Cancelling out 6000/6080 as almost 1, this would have left 'Gradient = ROC/GS' or 'RoC = Gradient x GS', which is what is taught and examined in both Gen and Radio Nav.

    I stand to be educated by your good self.

    All the best,


    Best Regards,

    Tony Pike

    Give Sergei back his dignity......Simples!

  • #2
    I think I have the's to do with Gross and Net Gradients, n'est ce pas?
    Best Regards,

    Tony Pike

    Give Sergei back his dignity......Simples!


    • #3
      No, its nothing to do with that. Clearly rates of climb and descent on the VSI have nothing to do with groundspeed, they just show the vertical rate of ascent or descent. The diagrams in Principles of Flight and Performance correctly show the relationship between TAS on the hypotenuse of a triangle and with rate of climb on the opposite side of the triangle to the climb angle.

      When you are calculating the required rate of descent on the glideslope you doing something different, you are calculating at what rate you should lose height to get through 'x' feet in a given time. The groundspeed is relevant to this because that, and the distance to go, control the time you have available.

      You could build the rate of descent formula like this, starting with, say, height 'h' in NM and distance 'd', same units:

      Time to touchdown in minutes = 60 x (d / groundspeed)
      height in feet = h x 6080

      required rate of descent = height in feet / time to touchdown in minutes

      rate of descent = [h x 6080] / [60 x (d / groundspeed)]
      so rate of descent = [groundspeed x 6080 x (h / d)] / 60

      now you will recognise that h/d is the tangent of the glide angle, and you know that for small angles this is approximately the angle over 60 so, substituting again, we get

      rate of descent = (glide angle / 60) x (groundspeed / 60) x 6080

      which is the approved formula,

      and which contracts down to 5 x the groundspeed by assuming a glide angle of 3 degrees and approximating the 6080 to 6000.


      • #4
        Stunning job. Thank you Alex.
        Best Regards,

        Tony Pike

        Give Sergei back his dignity......Simples!