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# canopy question regarding the math

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i was looking up something in the sim and got sidetracked pretty good this morning.  reading the canopy piloting part on page 123, there is a diagram of the canopy and the arrows indicating the various forces.  i recall some of the math involved from high school, like velocity is perpendicular to lift, but then is says speed is a magnitude of velocity.  i can get that, but i thought that speed was perpendicular to gravity, and not the same direction as velocity.  i also thought that energy increased as the square to the velocity, not speed.  is that just me being pedantic and misunderstanding the relative terms, or something deeper?  i have enough distractions not to go searching for the answer myself.  i could lose all week on this if i'm not careful.

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Speed is a scalar quantity which means it does not have a direction like the vector quantity velocity does.

Energy is also a scalar quantity, and when people talk about squaring velocity, they really mean squaring the magnitude of velocity (speed).

Momentum is a vector.

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so i was thinking of momentum not speed.  i'm starting to look at fluid dynamics and need to refresh my core math first it seems.  some of that shit is confusing as hell, but i'll get it, i always do.  if you had any links to help it would be appreciated though.

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On 11/22/2021 at 7:59 AM, sfzombie13 said:

i recall some of the math involved from high school, like velocity is perpendicular to lift, but then is says speed is a magnitude of velocity.  i can get that, but i thought that speed was perpendicular to gravity, and not the same direction as velocity.  i also thought that energy increased as the square to the velocity, not speed.

Lift is the net force acting on an aircraft to oppose gravity; it always acts perpendicular to the oncoming flow.  In stabilized and fixed-altitude flight, lift exactly cancels weight (mass times gravity.)  However, if you're in a turn, the lift vector is no longer vertical; it now points a little in the direction of the turn, and is the force that causes the aircraft to change its momentum vector.  Also if you are descending it tilts forward a bit.  That's why ram-air parachutes glide, because the lift vector provides you with some forward force to maintain your speed (against your drag.)

The term "speed" is fraught with peril when talking about airspeed.  Indicated (IAS) airspeed is basically how much air you are passing through per second.  The higher you are, the less air there is, so the same speed gives you a lower IAS.  It also determines things like lift and drag.  Ground speed is how much ground you are covering, and can be different from IAS both due to altitude and descent angle.  The true airspeed (TAS) is how fast the aircraft is moving relative to the air around it; it is the closest to what you are talking about above.  But that only matters with respect to the air you are in.  If you're about to hit the ground, what you care about is your velocity vector relative to the ground, and like you mention the energy goes up as the square of (relative) speed.  And even then you probably care more about the vertical component of that velocity vector rather than the horizontal component (or even total magnitude.)

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