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Tapered Barrel Volume

A while ago, my parents’ neighbor asked a good question: For a tapered barrel, is there an equation for the volume versus height? Here’s what I came up with.

When comparing the volume ratio for specific barrels, the following fill curves occur:

Tapered-Barrel

Now holding a constant maximum radius, the following absolute volume ratios (compared to the straight sided barrel) occur:

Tapered-Barrel-2

Rules of thumb:

  • The fill-volume ratio is approximately (±15%) linear with height when the upper to lower radius ratio is within 2:1.
  • Half the volume of a cone is at the 20% height level.

The final recommendation was to fill the barrel with a known volume (gallons) and mark the side.

Crimson Aviators Photo

Crimson Aviators Cookout 2015

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The Crimson Aviators university student club holds regular meeting at the Tuscaloosa Alabama airport (KTCL). The club is operated by University of Alabama students. I am the faculty adviser on the far right. More information is available at Crimson Aviators.

Thanks to Abe Alibrahim at www.generalaviationcenter.com for hosting the club, and providing generous hanger space for meetings. For aircraft rentals and flight training in the Tuscaloosa area, contact Abe at 205-345-5900.

How the future of drones is set in the past

How the future of drones is set in the past.
or
How one event 100 years ago will replay again.

The date was 1915. The place was Western Europe. The event was the arrival of aircraft meant to kill. This was the birth of fighter aircraft. Before that time, military aircraft were used as spotters. In the US – Mexican “Border War” (1910-1919), the US Army first fielded aircraft; Mexico fielded no opposing aircraft. In 1914, the nature of aircraft changed and evolved into three standard categories: observation, bombers, and fighters. (As an aside, the transport came later.)

We can pin the date of which the fighter aircraft came of age: The Fokker Scourge, July 1915. The critical question for the 21st century is, “What is the drone analog of the machine gun interrupter?”

Will  drones kill drones? In a word, yes.

Well, we know that on a traditional symmetrical battlefield, everything that flies will be hunted. Both bird and machine will be eliminated ruthlessly.

But on the asymmetrical battlefield and the rule-of-law environment, the nature of drones will become extraordinary. Expect bio-mimicry to make drones functionally and visually indistinguishable from bird, insects, and plant matter. The great hunt will be classification and potentially elimination of the unwanted machines. EM transmissions will be a giveaway and will either result in high gain antenna systems with burst transmissions (aka. WW2 submarines)  or fully autonomous vehicles. The whine of a propeller, gearbox, or motor will be a dead giveaway.

How will drones kill drones? Ruthlessly autonomously. Hawks vs. Watchbirds

Solving a Convection PDE

The problem under consideration is a linear convection PDE.

\(\) From Farlow’s “Partial Differential Equations for Scientists and Engineers”, chapter 15 problem 3 is $$u_t = -2u_x \quad -\infty < x < \infty \quad 0<t<\infty $$$$ u(x,0)=e^{-x^2}$$

Intuition

We see that the governing equation is a linear convection problem. The characteristic velocity is 2. We expect the solution to be a shifted initial condition $$u(x,t)=e^{-(x-2t)^{2}}$$

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Standard Atmosphere and Airspeed

This post provides a visual characterization of a generic flight envelope with a standard atmosphere. The following figure shows a generic flight envelope map.

KCAS, TCAS, Mach, Dynamic pressure, Temperature

Atmosphere and Airspeed

A pdf version is available at airspeed-2014c.pdf. This file plots altitude (0 to 50 thousand feet), calibrated airspeed (0 to 1000 KCAS), true airspeed, Mach number, dynamic pressure, static pressure, and total temperature on one handy page.

Airspeed:

Engineers and pilots track three different speeds:

  1.  Calibrated Airspeed: the airspeed from the pitot system corrected for instrument bias
  2. True Airspeed: actual speed through the air
  3. Groundspeed: speed referenced to level ground

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F-35 Economy of Scale

Photo (c) Andy Wolfe

Photo (c) Andy Wolfe

The F-35 Joint Strike Fighter (JSF) was conceived as a 5th generation fighter with a tri-service economy of scale. The late 1990s philosophy is stated as: “The rising unit costs of military aircraft and the new emphasis on greater commonality of aircraft designs among the services tended to push procurement trends toward ever smaller numbers of even more complex and expensive fighters designed to offer multirole and cross-service capabilities. [1]” A post-design analysis by RAND 20 years later estimates that the JSF’s life-cycle cost is 65% higher than a single-service fighter rather than the promised 16% lower life-cycle cost [2]. As of mid-2014, the F-35’s flight envelope is restricted to Mach 0.9, 3 g’s, and 3 hours between engine inspections [3]. Question: what is the subsequent impact to F-16 and A-10 mission replacements if the F-35 program continues having fielding issues?

[1] M. Lorell and H. Levaux, The Cutting Edge: A Half Century of U.S. Fighter Aircraft R&D, RAND, 1998.

[2] M. Lorell, M. Kennedy, R. S. Leonard, K. Munson, S. Abramzon, D. An and R. Guffey, Do Joint Fighter Programs Save Money?, RAND, 2013.

[3] A. Mehta, “Some F-35 Flight Restrictions Lifted,” DefenseNews, 2014. [Online]. Available: http://www.defensenews.com/article/20140729/DEFREG02/307290036/Some-F-35-Flight-Restrictions-Lifted.

The amazing Dassault Mirage III

300px-RAAF_Mirage_III_1

Photo by TSGT CURT EDDINGS

The Dassault Mirage operational career spans 50 years in its many variants: mid 1950s until 2014. By modern standards, the aircraft design is exceptionally simple yet particularly capable.

[The Mirage III] was the first French aircraft to incorporate area rule technology and the first to exceed Mach 1.5 in flight. Nevertheless, Dassault employed only 14 engineers and draftsmen in its design and only 70 shop fabricators in its assembly…. The pre-production Mirage III A, which first flew in May 1958 reached a speed of Mach 2.2 and an altitude of 82,000 feet one month later. It differed from the earlier prototype chiefly in having an improved flight control system and somewhat more powerful Atar engine. [1]

The design time to first flight was an astonishing 9 months [1]. Dassault’s design groups operated on an incremental modification and prototype strategy. Designs failing to reach viability or exhibiting increasing risk were terminated cheaply and quickly (i.e. Mirage III G, variable sweep version). The Mirage was sold worldwide for many decades.

[1] R. Perry, A Prototype Strategy for Aircraft Development (RM-5597-1-PR), RAND, 1972.

Work of Art?

What is a work of art? Can engineers create works of art? Or are creative works of art solely seen in performance arts?

This is the question under consideration in this post. Let us review some images.

http://www.bugatti100p.com/

http://www.bugatti100p.com/

"Hughes H-1 Racer Replica Oshkosh 2003" by FlugKerl2 - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Hughes_H-1_Racer_Replica_Oshkosh_2003.jpg#mediaviewer/File:Hughes_H-1_Racer_Replica_Oshkosh_2003.jpg

Hughes H-1 Racer

"HughesH1RacerTailTip" by 350z33 (talk) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:HughesH1RacerTailTip.JPG#mediaviewer/File:HughesH1RacerTailTip.JPG

Hughes H-1 Racer Tail

"North American F86-01". Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:North_American_F86-01.JPG#mediaviewer/File:North_American_F86-01.JPG

F-86

It seems that engineers don’t need to join a performance art troupe to create works of art.

Rapid Analysis of a Reverse-Engineered Aircraft

Full memo: AEM495-2014-M02-revA

This post concerns a reverse engineered CAD model of the Cessna Citation 2. The objective of this memo is to provide a quick evaluation of the model with respect to the aerodynamics.

The model was supplied in a .STEP format by GrabCAD.com. It should be noted that the loft geometry presented is not an official Cessna geometry; the geometry was solely determined by reverse engineering. The as-supplied model required moderate loft-cleanup and surface trimming with CATIA. The cleaned model is illustrated in Figure 1. The forward hatch area was particularly difficult as the original model attempted to represent the hatch gaps with a tangential double fillet.

citation-cad

Figure 1: Citation CAD model (full aircraft)

A significant loft issue in the canopy area was spotted with zebra lighting (see Figure 2) at the intersection of the cylindrical fuselage and the complex canopy surface. From the zebra lighting, this region does not appear to be either tangentially or curvature constrained. This canopy loft issue will appear as a local accelerated flow region with detrimental downstream separation. A comparison with the actual Citation surface reveals that the current CAD model poorly represents reality.

citation-m080a0-iso-contour

Cp Contours: Mach 0.80, AOA 0

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