Question: tl;dr: trying to find propeller efficiency with thrust, velocity and power and see which propeller length to pitch ratio is efficient.

Hello, I'm a high school student working on an extended essay for my physics class. What I've basically done is took a bunch of propellers (7x4E, 7x5E, 7X6E, so on and so forth). Propellers of lengths: 7, 8, 9, 10 inches and pitches: 4, 5, 6, 7, 8. (Fixed pitch propellers).

I've taken these propellers and hooked them up to a motor and a weighing scale to try and find how much thrust they produce. Then, I put them on to a control line aircraft to see how fast the plane goes.

Basically, Im trying to find the efficiency of these propellers and the data I have is the thrust produced by the propeller at different power levels and the velocity at different power levels. I'd really like to know if there's a relationship that I could employ to find the efficiency!

It doesn't have to be complex! Just needs to work from a physics standpoint. My deadline's coming up soon and any help would be greatly appreciated.

Answer: 
The FAA states that a [Ceiling](https://www.ecfr.gov/current/title-14/chapter-I/subchapter-A/part-1/section-1.1) "means the height above the earth's surface of the lowest layer of clouds or obscuring phenomena that is **reported** as “**broken**”, “overcast”, or “obscuration”, and not classified as “thin” or “partial”. A [broken level](https://w1.weather.gov/glossary/index.php?word=broken) is defined by the National Weather Service as "A layer of the atmosphere with **5/8 to 7/8** sky cover (cloud cover)."

*(emphasis is mine)*

This means that 4/8ths of the sky can be clear and the **ceiling** would be **reported** as **broken**. (see the image below of a ceiling)

14 CFR Part 91.155(c) states:

> 
> (c) Except as provided in § 91.157, no person may operate an aircraft beneath **the ceiling** under VFR within the lateral boundaries of controlled airspace designated to the surface for an airport when the ceiling is less than 1,000 feet.
> 
> 
> 

*(emphasis is mine)*

In my opinion, this means that when the *official* **ceiling** is reported (in a METAR, for example) as "broken" (for example) this would apply to all airspace below the reported ceiling value within the entire "...lateral boundaries of the controlled airspace designated to the surface for an airport..." (ref: 14 CFR Part 91.155 (c)).

Also, in my opinion, the official ceiling reported in a METAR, for example, is not a cloud or group of clouds directly above the aircraft measured and defined as a *ceiling* by the pilot. Instead, it is a defined and regulatory based atmospheric condition that, if it is reported as being below 1000 ft. AGL, renders the entire surface area of the controlled airspace below that reported ceiling as IMC.

So, although **some** surface areas of controlled airspace surrounding an airport may be large, 14 CFR Part 91.155(c), and the definition of a ceiling, do not make any distinction or allowance for relief just because there is no cloud cover directly above the aircraft.

*Image of a "Broken" ceiling (highlighting is mine).* [Source:](https://www.boldmethod.com/learn-to-fly/weather/how-cloud-ceilings-are-reported-for-pilots-metar/)

[![enter image description here](https://i.stack.imgur.com/LwMgo.png)](https://i.stack.imgur.com/LwMgo.png)
The language talks about operating "beneath **the ceiling** ... when **the ceiling** is less than 1,000'." If you're not beneath that sub-1,000' ceiling, then this language doesn't apply to you.

In your point 2, if there's no ceiling where you are, then you definitely aren't operating "beneath the ceiling."

Your point 1 sounds like the cloud layer is sloping up as you get farther from the airport, and the pilot knows (how?) that where he is, there is now more than 1,000' between the ground and the clouds, while your point 3 has the ground sloping up so that the space between the ground and the clouds has become less than 1,000' where the pilot is operating. Those points would boil down to asking if the definition of ceiling,

> 
> Ceiling means the height above the **earth's surface** of the lowest **layer of clouds** or obscuring phenomena that is reported as broken, overcast, or obscuration, and not classified as thin or partial.
> 
> 
> 

is related to the (clouds & earth's surface *at the airport* itself), or the (clouds & earth's surface *where you're operating*). I'll leave that distinction for a separate answer.