# Glide Slope Formula

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Hope you all had a nice Christmas.I am looking for a formula that will give me VS (vertical speed in ft)taking into account distance, ground speed and altitude.I don't want a formula for a 3% glide slope!The percentage of the glide slope is secondary.Example: Distance to threshold is 5 nm, Ground speed is 140 knots, Altitude is 2500 ft. What is the formula to calculate the Vertical Speed (VS) to land nicely on the threshold?Maybe you can point me to a site where I can find this.Thanks for your help Roelof

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Roelof,TimeToTouchdown = DistanceToThreshold / GroundSpeedVerticalSpeed = Altitude / TimeToTouchdownDoug

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I knew it would be easy but yet so difficult if you don't know.Thanks Doug. Saves me a lot of time. Have a prosperous 2007Roelof >TimeToTouchdown = DistanceToThreshold / GroundSpeed>VerticalSpeed = Altitude / TimeToTouchdown>>Doug

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Just remember DistanceToThreshold is the hypotenuse, not the distance across the ground... or your calculations will be a little bit off. ;)Other than that, it's basic geometry.

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Thanks Ed! Good to know. I hope FS9 XML understands the sqrt function.Roelof>Just remember DistanceToThreshold is the hypotenuse, not the>distance across the ground... or your calculations will be a>little bit off. ;)>>Other than that, it's basic geometry.

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If I wanted to calculate the glide slope angle without referencing a chart, how would I go about that? Assume I know my height above airport and distance to the airport. Thanks!~NateEdit - Oh my, I just realized the calculations I was doing are off because I forgot to convert to the same units. Distance is in NM (ergo nautical feet), height is in MSL, which is not nautical.

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>Thanks Ed! Good to know. I hope FS9 XML understands the sqrt>function.>>Roelof>>>Just remember DistanceToThreshold is the hypotenuse, not the>>distance across the ground... or your calculations will be a>>little bit off. ;)>>>>Other than that, it's basic geometry.>I understand it is distance across the ground because distance is in nmiles and speed is GROUND speed in nmiles per hour/minute; both are linear variables.Tom

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>>Thanks Ed! Good to know. I hope FS9 XML understands the>sqrt>>function.>>>>Roelof>>>>>Just remember DistanceToThreshold is the hypotenuse, not>the>>>distance across the ground... or your calculations will be>a>>>little bit off. ;)>>>>>>Other than that, it's basic geometry.>>>>I understand it is distance across the ground because distance>is in nmiles and speed is GROUND speed in nmiles per>hour/minute; both are linear variables.>>Tom>>Except the aircraft is not flying in a linear fashion. It is in a three dimensional space and traversing in two directions at once. While using the groundspeed and the linear distance will tell you how long until your aircraft crosses the threshold, it will not take into account the distance needed to travel downward to physically touch the threshold.To be honest, the mathmatical error is probably rather slight... but I never take those kinds of chances when coding.

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>Except the aircraft is not flying in a linear fashion. It is>in a three dimensional space and traversing in two directions>at once. While using the groundspeed and the linear distance>will tell you how long until your aircraft crosses the>threshold, it will not take into account the distance needed>to travel downward to physically touch the threshold.>>To be honest, the mathmatical error is probably rather>slight... but I never take those kinds of chances when>coding.Only "slight?" Try mininscule or nearly non-existant... :)At 1nm altitude and 20 nm distance from the threshold, the difference between the base and the hypotenuse is a whopping 0.02 nm...:-outta Typical FAF for an ILS approach is 2500' @ 5nm, which means the hypoteneuse is a tremendous 5.0168996nm... :-beerchug But you are right, because the math is so simple, there's no reason not to be 99.9% accurate... :-halo

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Hello!This works alsoAltitude 2500 ft = .41 nm, tan (glide path) = altitude / distance to runway = .0822; tan^-1 = Glide path angle = 4.70 deg; and for one minute VS, GS = 140 knots =14185.26 ft/min VS = tan (glide path) * GS = 1166 ft/min; Time to landing = Altitude / VS = 2.14 min.This way you get glide path, VS and TTL.Javier

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Ed, IMHO calculating the hypotenuse of the distance will lead to wrong results. Both distance to a point and ground speed are geopositional values hence altitude does not count here. For example, if ground speed is 100 nmiles per hour, in one hour the LINEAR (ground) distance traveled will be 100 nmiles no matter an a/c is climbing, descending or flying leveled. Then as gross reference, if linear distance is 100 nmiles, travelling at 100 nmiles per hour ground speed, starting at 100 nmiles high and descending at 100 nmiles per hour of vertical speed, an aircraft should reach the ground after one hour. Basic but I hope enough illustrative :-) Tom

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Well... I know for a fact I can trace different times based on whether you're climbing or descending.But... whatever. ;)

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Hi Roelof,I released a tiny tool gauge for these kind of calculations a while ago. It's in XML so you'll be able to read the code.I added the option to select the tuned NAV station (if it provides DME infos) and to calculate the necessary VC depending on the actual altitude and speed. It also offers a direct transfer of the calculation into the autopilot. Search for vscalc2.zip here at AVSIM.Good luck with your project!Herbert Pralle

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Well, when you say "land nicely" you would be talking about following the standard 2.5 deg glide slope.You can calculate the vertical velocity (a vector) required to reach the threshold given any arbitrary starting position, but that doesn't mean it will be one that would allow you to "land nicely". There is a reason that the standard is 2.5 degees.To answer your question as best I can, you are dealing with a right triangle: c^2 = a^2 + b^2is a good start.Basically, distance 'c' is the hypotenuse of the triangle defined by the distance to threshold, and the altitude.More importantly, if you are at altitude 'x' above the threshold, then you have time 't' to decend to that distance given your velocity is 'v': v = d/tso: t = d/vIn your problem, that means you have: 5 nm --------- = 2.14 mins 140 knotsto descend. Given the 1st formula above you then have to descend at the rate: v = 2500 ft / 2.14 mins * 60 seconds = 19.5 ft/secwhich is a very shallow descent.Generally, you are going to always make an approach so that if your engine quits you can make the runway and maintain the same angle of descent, ie. about 250 ft/sec.Your mileage may vary.

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Thank you all very much for contributing to this Vertical Speed formula. There is enough now to get me and other designers going.I wil also have a look at Pralle's VS calculator.Thanks a lot,Roelof

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Hi Herbert,Your e-mail address in the file seems to be invalid.I need to ask you something.Why 5 gauges. Is there a difference? They are all the same size. Can you enlighten me? Thanks for your time Roelof. >Hi Roelof,>Search for vscalc2.zip here at AVSIM.>>Good luck with your project!>>Herbert Pralle>

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