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#11




Koch Chart Formula
On 20060825, abripl wrote:
Your function was for Da = f(Pa, T) which in turn require various approximations to get takeoff distance and climb performance  not a finished product. Jim's formula were correct. The Koch chart, itself, contains no takeoff distance and climb performance. It is merely a translation, if you will, expressed in chart form of density altitude given pressure altitude and temperature. Any additions to any Koch chart, such as TO distance or climb performance, _are_ additions and may hold true for only for certain classes of aircraft. Generally what you see in charts with those additions might have been created and would probably work for the typical SE general aviation plane. To this extent they may be very useful and helpful. But, again, they are _not_ part of the Koch chart, they are _additions_. ....Edwin  __________________________________________________ __________ "Once you have flown, you will walk the earth with your eyes turned skyward, for there you have been, there you long to return."da Vinci http://bellsouthpwp2.net/e/d/edwinljohnson 
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#12




Koch Chart Formula
Edwin Johnson wrote: On 20060825, abripl wrote: Jim's formula were correct. .... Ed, I am not debating Jim's prescription correctness, just mathematical function usefulness. I posted the original post and asked for a math function to represent the Koch chart. Jim did not do that but gave the Da = f(T,Pa) function and then we need to add more to it. The Koch chart, itself, contains no takeoff distance and climb performance. ....... Aw come on. All you have to know is your sea level T.O. and Climb and just multiply by Koch chart factors. Very simple one step process..... And it easily goes to 10K dens. alt. Does anybody know Mr. Koch? Surely somebody made the chart up originally? 
#13




Koch Chart Formula
"abripl" wrote in message
ups.com... [...] Does anybody know Mr. Koch? Surely somebody made the chart up originally? You could make such a chart from scratch fairly easily, using empirical methods. For an airplane that has published performance figures for different density altitudes, it's especially easy. For one that does not, you'll have to do some flight testing to obtain those figures, but once you have them, the process is the same. If you know the *exact* performance characteristics of a given airplane, it is possible to come up with some pretty precise formulae describing that airplane's performance at various altitudes. But getting that data is difficult, and unless you have access to a vast engineering database of engines, prop and wing airfoils, drag coefficients, etc. you're unlikely to be able to. But empirical data is relatively easy to come by. Fly the plane, take notes, viola. Of course, someone already did all that, and they made a chart out of it. I gather from your previous post that your approach was to attempt to parametrically combine all of the factors into a single equation, but I'm not convinced that's the right approach, at least not initially. You actually have a couple of equations, based on the same lineintersection equation that can be based on the chart that's already published. But that equation isn't going to take the form "(aT + bP + c)^d". You've got a line equation defined by the two endpoints (temperature and pressure altitude), intersecting with the vertical axis at some point. That gives you a vertical coordinate that can be used logarithmically (takeoff distance) or exponentially (climb rate reduction) to determine the actual correct factor found on the chart. The actual Cartesian coordinates for the graph and the base or exponent (as appropriate) are derivable from the existing chart, simply by measuring the chart and mapping it back to the original numbers. But you're not going to get an equation of the form "(aT + bP + c)^d"...you'll get one linear equation that gives you the point of intersection, and then two other equations (one log, one exp) to map that to the actual performance adjustments. Of course, even after you do all that, all you've got is a mathematical description of the Koch chart. It's not going to tell you the *actual* performance variations for a given airplane. It's just going to give you the same (generally conservative) rules of thumb that the Koch chart provides. Pete 
#14




Koch Chart Formula
Sorry, I wasn't aware I was teaching freshman high school Algebra 1 here.
The "final product" is a series of four equations, two for fixed pitch and two for constant speed propellers. I will derive/illustrate the first one. It is left as an exercise for the student to complete the other three (hint  you only have to change one number in the equation). D = Density Altitude (from the prior equation). TD = Takeoff Distance at D TS = Takeoff Distance at sea level % = The percentage increase figures from the prior document. For example, for a fixed pitch propeller: TD = TS * (1 + ((D / 1000) * 0.15)) Jim "abripl" wrote in message oups.com... Your function was for Da = f(Pa, T) which in turn require various approximations to get takeoff distance and climb performance  not a finished product. I may try again later to get a better empirical function  not impossible. RST Engineering wrote: did you not get the exact equations I posted here two days ago? Jim 

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