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Graphs of power coefficient ($C_P$), thrust coefficient ($C_T$), and efficiency ($\eta=JC_T/C_P$) of the 5868-R6 propeller as functions of advance ratio ($J=V/(nD)$) and propeller pitch (blade angle at 0.75R?) are found in many textbooks (such as McCormic):

Power coefficient

Thrust coefficient

enter image description here

From these curves it seems that for a given propeller pitch $C_P$, $C_T$, and $\eta$ go to zero at the same value of $J$. At also seems that the slopes of the $C_T$ vs $J$ curves for higher value of $J$ (where $C_T$ approaches zero) are the same.

I have two questions:

  1. Do $C_P$, $C_T$, and $\eta$ always go to zero simultaneously at the same value of $J$ for all propellers? Why?
  2. Are the slopes of the $C_T$ vs $J$ curves where $C_T\rightarrow 0$ the same for all values of propeller pitch?
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  • $\begingroup$ If $C_T$ is 0, then by the definition of $\eta=JC_T/C_P$, $\eta=0$, irrespective of the value of $J$. $\endgroup$
    – ROIMaison
    Commented Dec 6, 2016 at 15:38
  • $\begingroup$ Yes @ROIMaison, that answers one part of the first question. If $C_T=0$ at $J=J_0$, then $\eta=0$ at $0$ and at $J_0$. :-) $\endgroup$
    – Christo
    Commented Dec 6, 2016 at 16:20

1 Answer 1

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Do $C_P$, $C_T$, and $\eta$ always go to zero simultaneously at the same value of $J$ for all propellers? Why?

Yes; Talking in dimensional quantities, This speed, at which all coefficients goes to zero is called pitch speed.

At pitch speed thrust goes to zero due to the fact that the incoming airflow drives the apparent angle of attack seen by the blades to zero.

Power = Thrust * velocity , As thrust goes to zero power goes to zero as well.

Efficiency $\eta = \frac{P_{out}}{P_{in}}$, $P_{out}$ goes to zero as shown above hence $\eta$ goes to zero.

HTH

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  • $\begingroup$ Thank you for the answer to the first part of my question, @ABCD. Any thoughts on the second part? $\endgroup$
    – Christo
    Commented Mar 28, 2018 at 12:14
  • $\begingroup$ Hi @Christo, sorry Im not clear what do you mean by the second part. Ct will always be some finite value. it doesnt go to infinity $\endgroup$
    – ABCD
    Commented Apr 2, 2018 at 5:09
  • $\begingroup$ Sorry, @ABCD! It was a typo; I edited the question. It should be the slope of CT vs J as CT decreases to zero. $\endgroup$
    – Christo
    Commented Apr 2, 2018 at 18:17
  • $\begingroup$ HI @Christo, Not really, the slope depends on the pitch/diameter ratio. You can see this trend in your second image attached. The reason is for a given RPM and diameter, higher pitch propeller has higher pitch speed and hence shallower slope. HTH $\endgroup$
    – ABCD
    Commented Apr 3, 2018 at 10:54
  • $\begingroup$ Does a negative power coefficient have any meaning? I.e. can the curves be said to "continue" below the X axis in any meaningful sense? Asking because in the configuration tables for Microsoft Flight simulator engine and propeller combinations, the table that gives the power coefficient values for different advance ratios and propeller pitch angles, the power coefficient is negative for high J values. $\endgroup$
    – tml
    Commented May 3, 2021 at 22:26

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