en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

2012-12-11T15:03:01Z

clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

← Older revision		Revision as of 17:03, 11 December 2012
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			'''Vertical penetration''' is a [[Scalar (mathematics)\|scalar]] measurement of [[distance]], of the maximum altitude an object, most often an [[aircraft]] can gain at any particular moment in time, thereby converting all of its energy from [[Kinetic Energy\|kinetic]] to [[Potential Energy\|gravitational potential]].

			It is worth noting that when listing an aircraft's technical specifications, ''vertical penetration'' can be appropriately used in substitution of ''maximum vertical penetration''.

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			Assume an aircraft has the same [[mechanical energy]] at two separate points in its flight - one when the aircraft is straight and level, holding a constant [[airspeed]], and negligible [[altitude]] (''near'' zero potential energy) and the other, following a sudden 90 degree [[Flight dynamics\|pitch]] increase in attitude, when the aircraft has noticeable [[altitude]], and negligible airspeed (zero kinetic energy). Assuming the aircraft can 100% efficiently convert all of its kinetic energy to potential (theoretically have a radius of 0 in the turn, refer to [[centripetal force]]), the aircraft has the same mechanical energy in both points, the kinetic energy of the first point equaling the potential energy of the second:

			<math>\,mgh_2 = \frac{1}{2}mv_1^2</math>

			where ''m'' is the mass, ''v'' is the speed, ''h'' is the height of the body, and ''g'' is the is [[standard gravity]]. In [[SI]] units (used for most modern scientific work), mass is measured in [[kilogram]]s, speed in metres per [[second]], height is in metres, standard gravity in [[Metre per second squared]], and the resulting energy is in [[joule]]s.

			Notice that neither mass nor standard gravity were given subscripts indicating which point they correspond to. This is because both are assumed constant. This is mildly incorrect for both. As an aircraft operates, it consumes fuel, oil, etc., which slightly decreases mass. And since the standard gravity is inversely [[proportionality (mathematics)\|proportional]] to the distance between the body and Earth, and the aircraft is gaining altitude (increasing said distance), slightly decreasing standard gravity.

			By dividing by standard gravity and mass, and rewriting <math>\,h_2</math> as <math>\, \Delta h</math>, as <math>\,h_1 = 0</math> shows that:

			<math>\Delta h = \frac{\frac{1}{2}mv_1^2}{mg}</math>

			by canceling out mass, and rewriting <math>\,v_1</math> as simply <math>\,v</math> as point two has no velocity, and moving the <math>\frac{1}{2}</math> to the denominator, the formula for vertical penetration has yielded:

			<math>\Delta h = \frac{v^2}{2g}</math>


			[[Category:Aerodynamics]]

en>Bhugh: added ref to Cauchy-Davenport theorem

2012-06-20T14:38:05Z

added ref to Cauchy-Davenport theorem

New page

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Dyson's transform - Revision history

en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8797)

en>Bhugh: added ref to Cauchy-Davenport theorem