This engineering talk discusses aerodynamics, lift generation, and a couple of common myths that persist in the aviation community. The talk was presented at the July meeting of the Texas Flying Club (http://www.texasflyingclub.com/). As a general guideline, the audience was comprised of pilots, such that the mathematics and physics are not presented as a formal proof but presented with the intent to convey understanding. One key point made is that any discussion of aerodynamics concepts must be consistent with continuity of mass, momentum, and energy. A simple freestream, source/sink, and vortex model was presented to explore a consistent understanding of aerodynamics for aviation.
One Vortex to rule them all, One Vortex to find them, One Vortex to bring them all and in the darkness bind them In the Land of Aerodynamics where the Myths lie
How does surface roughness including frost and flaking paint affect aerodynamics? In this note, I take a look at the physics and the drag and stall characteristics of frost and flaking paint. A flight test of two Cessna 172s indicates the surprisingly large relative drag increment of flaking paint.
This engineering note discusses the commercial checkride 8s on pylons maneuver. The governing physics are used to derive the pivotal altitude and two strategies for adjusting the maneuver for lower powered aircraft.
In this engineering talk to the Texas Flying Club, I discussed maneuvering speed (aka corner velocity). This talk includes a discussion of the physics, applied calculations for the club’s Cessna 172 with a 2400 pound STC, references and discussions of the CAR 3 regulations governing most older aircraft, and a discussion of limitations of the regulations.
The important points to remember are:
Maneuvering Speed only effectively protects against a SINGLE control input.
Reduce Va at lower weights. A good rule of thumb is a reduction by half the weight ratio.
Negative load limits and maneuvering speed are less than the positive load limits and Va.
The Rocket Equation is a fundamental solution for rocket conceptual understanding and development. But did you know that there is an analytical solution to the distance, the integral of the rocket equation?
ΔV Solution
The ideal rocket equation links the change in velocity ΔV to the propulsion system’s effective exit velocity and the mass fraction. We often see these written in terms of the specific impulse Isp.
The critical conceptual points are that the velocity change depends linearly on Isp but non-linearly with the mass fraction. The trivial zero fuel case (i.e. final = initial) has a natural log of 1 which computes to a velocity of zero. As Gus Grissom says, “No bucks, no Buck Rogers.” Adding fuel increases the rocket’s velocity change, but only in a log proportion to the fuel added. The concept boils down to one concept: Accelerating fuel requires fuel.
The rocket equation is valid across the propulsion burn, such that the instantaneous ΔV is computed from the burn parameters. If we compute the final mass as:
then ΔV(t) as a function of time is
The second form consolidates the terms into two canonical parameters: (1) a propulsion term with Isp, and (2) a mass flow ratio to the initial mass. Implied in this form is the need to calculate the total burn time. The total burn time multiplied by the mass flow rate is the total propellant available, such that the final delta V is only a ln function of the ratio of propellant to initial mass and a linear function of the Isp. The following figure shows the delta V versus time for two different propellant mass flows.
Integral Distance Solution
Now for the rest of the story. The integral of ΔV(t) is the rocket distance, which has an exact analytical solution. We will start with the canonical form from above.
Now, the rate of change of distance is velocity, such that the differential distance versus differential time relationship is:
An analytical integral is available for this form, such that the distance traveled as a function of time when starting from rest in empty space is:
This can be particularly useful for verification of rocket solutions.
