sheaf theory - Descent of Morphisms of Sheaves

While reading Brylinski I am trying to understand the descent of morphisms of sheaves.In trying to form a new definition of a presheaf $A$ over a space $X$, we associate to each surjective local homeomorphism $f:Y \to X$ a set, denoted $A(Y\xrightarrow{f}X)$. The "restriction" condition of a presheaf amounts to: given a surjective local homeomorphism $g:Z \to Y$ we have a pullback map $g^{-1}:A(Y\xrightarrow{f}X) \to A(Z \xrightarrow{fg}X)$. The transitivity property for these "restriction" (pullback) maps is that given any diagram $$W \xri...Read more

ag.algebraic geometry - What is descent theory?

I read the article in wikipedia, but I didn't find it totally illuminating. As far as I've understood, essentially you have a morphism (in some probably geometrical category) $Y \rightarrow X$, where you interpret $Y$ as being the "disjoint union" of some "covering" (possibly in the Grothendieck topology sense) of $X$, and you want some object $\mathcal{F'}$ defined on $Y$ to descend to an object $\mathcal{F}$ defined on $X$ that will be isomorphic to $\mathcal{F}'$ when pullbacked to $Y$ (i.e. "restricted" to the patches of the covering). To d...Read more

How far from the runway should a small plane start its descent from 5000ft?

I don't fly, don't have a clue. But one of the main characters in my book DOES: it's a Cessna 152, just him at 14 stone and a couple of small bags, all conditions are perfect and he's flown from about 140 NM away. Would 5000ft be about the right altitude?The question is: how far away is the runway (a grass one on an unlicensed airfield) when he starts his descent? It's a direct approach, no pattern....Read more

descent - What would the altitude profile for a typical airline flight look like?

It's hard to appreciate an aircraft's rates of change in altitude, in particular with respect to its travel through the mass of air, rather than over the ground, since the latter is affected significantly by wind-speed (the distance an aircraft travels with respect to the ground is highly variable, compared to the distance it travels with respect to the air around it). Then, when climb profiles are plotted, it's always on a graph with a hugely compressed horizontal axis (naturally, because it's hard to discern much information when one axis is ...Read more

descent - Is it possible to fly 'in neutral'?

Sometimes, when I am driving, I knock the car 'out of gear' or set the stick to the neutral position, to save fuel. This is most easily done when cruising down a hill or when you have some good speed and are approaching a stopping point, i.e an intersection.Is there a flying equivalent for pilots? I'm wondering if during descent, or even a landing, fuel could (safely) be saved by reducing thrust to zero and gliding....Read more

What is the maths behind the descent rate calculation?

The descent rate calculation states that descent rate is calculated by 'groundspeed / 2 * 10'. Another document stated that the ground speed should be multiplied by 5 (or more accurately 5.2) to acquire the descent rate. The 5.2 value is found by finding the gradient for 3 NM for 1000 feet (based on the 3:1 glide ratio), which is 5.2% (found using tan of 3 degrees). The document can be found here: https://www.ivao.aero/training/documentation/books/SPP_APC_Top_of_descent.pdfMy question is: How was the formula created? It's interesting that I can...Read more

high altitude - What are the FAA regulations concerning controlled descent of a light payload?

I'm part of a High Altitude Ballooning club. Our main goal for this year is to achieve controlled descent of our payload. We plan to use Magnus force cylinders to go about this. I have found nothing in FAA documentation that specifically mentions something of this sort requiring extra clearance, but am still somewhat worried about putting the payload 100,000 feet up and then dropping it down in a controlled manner without being absolutely certain, as an object falling out of the sky in a directed manner could obviously garner concern if people ...Read more

nose - What does this statement about steep descent mean?

Source: Wolfgang Langewiesche - Stick and Rudder; An Explanation of the Art of FlyingIn the first chapter the author mentions, in a glide, if you want to descend more steeply, you want to want to point your nose less steeply.And if you want descend less steeply you point your nose more steeply. What is the reason for this?...Read more