UBUCIKO
UBUHLE NEMPILO
UBUCIKO BEZANDLA
AMASIKO NOMLANDO
EZOKUZIJABULISA
IMVELO
UKUDLA NEZIPHUZO
REVERSE ENGINEERING
IZAYENSI
EZEMIDLALO
UBUCHWEPHESHE
IZINTO EZIGQOKWAYO
Youblob (generated from this blueprint's notebook) · CC0
The Betz Limit: Why No Rotor Takes More Than 16/27 of the Wind
A wind rotor makes power by slowing the wind. Slow it too little and most of the energy blows through; slow it too much and the air piles up and goes round the rotor instead of through it. Between the two lies a best amount, and it caps every rotor that has ever been built at 16/27 — 59.3 % — of the power in the wind.
Albert Betz published the result in 1919–20; Frederick Lanchester and Nikolai Zhukovsky reached it independently, and it is sometimes given all three names.
This practice rung derives the limit in a notebook and uses it to rate the small rotor built in the first rung of this batch.
Oqalayo
About 2 hours
Imiyalelo
1
1
Derive the limit
Derive the limit
Ilayisha incwadi ye-Jupyter…
2
2
See the slowed wake
See the slowed wake
Set the rung-1 rotor in front of the box fan and hold a smouldering incense stick just upstream of the rotor disc, then just downstream, and watch the smoke. Measure the wind speed with the anemometer a rotor diameter in front, and a rotor diameter behind — with the rotor loaded, and then with the load disconnected so it free-wheels.
The loaded rotor leaves a slower wake than the free-wheeling one: slowing the air is where the power comes from. The notebook says the best wake is one third of the incoming wind; see how close your rotor's gets.
Izinto zokwakha zalesi sinyathelo:
Izinduku zempepho zokubona intuthu2 izicucuAmathuluzi adingekayo:
Ifeni yebhokisi (isivinini esiguqukayo)
I-anemometer yesandla
Ithephu Lokulinganisa3
3
Rate your rotor against Betz
Rate your rotor against Betz
From the first rung's measurements, take the electrical power at one wind speed. Divide it by the wind power through your rotor's disc at that speed (the notebook prints it): that is your Cp. Divide again by 0.593 to see what fraction of the theoretical best you reached.
Expect a small printed rotor on a hobby motor to reach only a fraction of the Betz limit: the motor's own losses, the blade drag at low Reynolds number and the tip losses all take their share. That gap is what a century of blade design has closed.
Amathuluzi adingekayo:
Isilinganisi sikagesi esiyinhlanganiselaI-anemometer yesandla4
4
Context
Context
**Albert Betz**, Göttingen, published the limit in 1919–20. It uses nothing but conservation of mass, momentum and energy through an idealised disc, which is why it applies to every kind of rotor — Savonius, Darrieus and propeller alike (the next two rungs). It is a practice rung: no patent anchors it.
**Honest limits of the model.** It ignores the swirl a rotor leaves behind, blade drag and tip losses — all of which lower the real figure further. It applies to an open rotor in a free stream; a rotor in a duct or a pipe (the Kaplan turbine) is a different problem.
Izinto
1- 2 izicucuIsibambeli
Amathuluzi Adingekayo
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