Map Sapling Learning macmillian leaming The German Me-163 Komet was built by the
ID: 3280618 • Letter: M
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Map Sapling Learning macmillian leaming The German Me-163 Komet was built by the Messerschmitt company during WWll. It was the only rocket powered military plane to ever be used in combat. The Komet set numerous flight records during the war and is considered an engineering marvel. Its record- setting combat speed made it a difficult target to shoot down However, the Komet burned fuel at an enormous rate. Typically, it would run out of fuel after 8 minutes of flight and have to glide back to base unpowered gliding level flight 220 574.0 mph exhaust 1855.0 kg 3855.0 kg Va stionnaires filled out by visitors. One A national aerospace museum has accumulated the results of question appears seeminly unanswered: How fast did the Me-163 glide back to base? Allied fighter pilots claim the glide speed was as low as 250 mph, whereas the few surviving German pilots claim closer to 360 mph. Both sides agree that the glide angle was about 22.0 with respect to the horizontal (as shown). The museum has asked you to settle the question theoretically The museum has provided a few facts that you can maybe use to calculate the glide speed. For one, the maximum thrust output of the rocket motor is well known, 1.80 x 104 N. At level flight (combat altitude) the Me- 163 traveled at a maximum speed of 574.0 mph Also, when filled with fuel, the Me-163 had a mass of 3855.0 kg, but dropped to 1855.0 kg once the rocket fuel ran out.Explanation / Answer
While the Me-163 was obviously designed for fast flight and thus was
streamlined alond its longitudinal axis (its x-axis; the axis of airflow), the problem
asks for its speed in the vertical axis (the z-axis) as it was gliding. There is a term
involved called "drag coefficient" that determines how much air resistance an
object has. I guessing that it has to be fairly high since the designers would want
the aircraft to be able to stay in the air for as long as possible while gliding.
Therefore, I will model the Me-163 as being similar to a flat plate perpendicular
to the airflow.
m = empty mass = 1855 kg
g = gravitational acceleration = 9.81 m/s²
W = empty weight = mg = 1855x9.81 = 18197.55 N
= average air density up to 9,000 meters = 0.80521 kg/m³
A = wing area = 18.5 m²
Cd = drag coefficient = 2.0
= glide angle = 22.0 °
Vv = vertical component of glide velocity = to be determined
Vh = horizontal component of glide velocity = to be determined
V = glide velocity = to be determined
Vv = [(2W)/(CdA)]
Vv = 34.95 m/s = 78.18 mph (vertical component)
tan = Vv / Vh
Vh(tan ) = Vv
Vh = Vv / (tan ) = 34.95/tan 22
Vh = 86.51 m/s = 193.51 mph (horizontal component)
V = [(Vv)² + (Vh)²]
V = 208.71 mph (glide velocity)
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