Rapid Derivation 5: The Lift and Drag Equations

This video is a part of a series of videos that show how specific aerospace engineering principles are derived. The goal is to keep the videos super short and straight to the point.
This video shows how the equations of lift and drag forces are derived using Buckingham's Pi-theorem.

[@adebimpesaheedolawale5471]

I read your text on propellers, but have problem solving example 14-18, I don’t know how you got an expression 6-2r/R for linear taper expression, I mean the c(r), I will be glad if you get back to me, is for my project, the topic of my project is adapting a gx200 engine for the propulsion of an aircraft, is the tapered blade, how do you came up with that expression

[@dr.gudmundssonaircraftdesign]

Hi Adebimpe. The expression is a linear parametric equation for a trapezoidal propeller blade and is obtained as follows: Imagine you have a propeller of diameter 2R. Further assume the theoretical blade has a chord of 6 inches at the center of rotation (where r=0) and 4 inches at the tip (where r=R). This means the chord changes linearly from 6" (at r=0) to 4" (at r=R). Thus, it follows that C(r) should be an expression of the form C(r)=Co+A∙r. The question is, what is the constant A? Well, if C(0)=Co=6 and C(R)=Co+A∙R=4, it follows that A=(4-6)/R=-2/R. Therefore, C(r)=6+(-2/R)r, which you can write as C(r)=6-2r/R. That's all there is to it. I hope this helps.

[@adebimpesaheedolawale5471]

@@dr.gudmundssonaircraftdesign you re my savior, thank you very much sir, one more question please My engine doesn’t have enough power, but I know what it’s can generated at that power, considering tapered and elliptical blade, I don’t know which one will generate more thrust, because am working on good thrust, any of your ideas will be highly appreciated

[@dr.gudmundssonaircraftdesign]

@@adebimpesaheedolawale5471 Unfortunately, there is not a simple answer to your question. It depends on the details of the planform geometry, blade twist, airfoil, airspeed and RPM. Since you were trying to solve Example 14-18, you were working on the blade element theory. It can answer your question, but first you must understand how it works through the spreadsheet. You also have to make sure you implement the induced velocity in the stream tube through the propeller. This is shown in Example 14-20. It allows you to compare thrust, efficiency, and power required to rotate the two props at your desired RPM and range of airspeeds. Best wishes.

[@adebimpesaheedolawale5471]

Thank you so much, really appreciate

[@adebimpesaheedolawale5471]

Sorry am disturbing you, I understand that a variable pitch propeller is like how much the propeller pitch is being twisted, but from the question above, we use 65% from the hub to 20% at the tip, is there a formulae behind those values or they re just assumptions, sorry for taking your time