Description

Calculus and NASA. Michael Bloem February 15, 2008 Calculus Field Trip Presentation. Outline. NASA’s (many!) uses of calculus Space Airfoil design My use of calculus at NASA Optimization for air traffic management. If then. Airfoil Design. FoilSim

Transcripts

Math and NASA Michael Bloem February 15, 2008 Calculus Field Trip Presentation

Outline NASA\'s (numerous!) employments of analytics Space Airfoil plan My utilization of math at NASA Optimization for air movement administration

If then

Airfoil Design FoilSim Pressure is change in compel per region On a wing, the lift is the contrast between the strengths following up on the base and top of the wing

Airfoil Design: Computing Lift

Airfoil Design: Computing Lift FoilSim says weight = 7731 lb How might I be able to enhance my gauge?

Traffic Flow Management Planning of air activity to abstain from surpassing airplane terminal and airspace limit, and viable utilization of accessible limit Cost of Delay to carriers in 2005 ~ $5.9 Billion (Air Transportation Association Estimate)

3D Visualization of Air Traffic

Air Traffic Flow Models Lagrangian Eulerian Keep track of every plane Keep track of the quantity of planes in various territories

Departures from Center i Outflow to Center j Region i Arrivals into Center i Inflow from Center j Aggregate Flow Model

Optimization with the Aggregate Flow Model Minimize: quadratic cost on the distinction between the booked and real entries and takeoffs Subject to: Follow framework elements conditions Do not have more total landings or flights than booked Count of air ship in every inside remains beneath a period differing most extreme Cumulative entries and takeoffs are non-diminishing

Optimization with the Aggregate Flow Model

How would we upgrade? Consider a straightforward case with one variable Check convexity: Set subsidiary = 0:

Another approach to upgrade? Newton\'s Method Find where subordinate = 0 Iteration: Why? Functions admirably on a PC Works well on huge issues (numerous factors)

Picture for Newton\'s Method

Newton\'s Method

Constrained Optimization What in the event that we have limits on x? Optimality condition for a curved capacity and a raised imperative set

Example of Constrained Optimization Constrained enhancement issue? Is it arched? Attempt our condition

Example of Constrained Optimization (proceeded)

Optimal Traffic Flow Management

Conclusions NASA utilizes math a considerable measure since analytics takes care of genuine issues

Websites Altair Lunar Lander CFD at Ames FoilSim Aviation Systems Division