**Design of a Lightweight Parachute for Military Use**A lightweight parachute is being developed for military applications. Key specifications include:- **Diameter $ D $:** 20 ft- **Total weight $ W $:** 190 lb (including payload, parachute, and equipment)- **Terminal settling speed $ V_t $:** 16 ft/s for the full-scale parachuteA one-twelfth scale model of the parachute is tested in a wind tunnel. The environmental conditions for the test (temperature and pressure) are identical to those for the full-scale prototype, set at 70°F with standard atmospheric pressure.### Tasks**a) Calculation of Drag Coefficient**- Determine the drag coefficient of the prototype with the assumption that at terminal velocity, the weight is balanced with aerodynamic drag.**b) Wind Tunnel Speed for Dynamic Similarity**- Establish the wind tunnel speed required to achieve dynamic similarity with the scale model.**c) Aerodynamic Drag Force on Model**- Compute the aerodynamic drag force acting on the model parachute within the wind tunnel in pounds.### Diagram OverviewThe provided diagram illustrates the parachute system. It includes the parachute canopy, the payload, and the effective terminal velocity $ V_t $. The diameter $ D $ is indicated at the top of the parachute.This structured approach to evaluating parachute dynamics ensures accuracy and performance under specified conditions.

(a) Write the properties of air at 70oF. ρ=0.07487 lbm/ft3μ=0.3797×10-6 lbf·s2/ft2 Here, ρ is the…

(Review experimental scaling) A lightweight parachute is being designed for military use. Its diameter D is 20 ft and the total weight W of the falling payload, parachute, and equipment is 190 lb. The design terminal settling speed V. (or terminal velocity) of the parachute at this weight is 16 ft/'s. A one-twelfth scale model of the parachute is tested in a wind tunnel. The wind tunnel temperature and pressure are the same as those of the prototype, which is 70 °F and standard atmospheric pressure. a) Calculate the drag coefficient of the prototype. (Hint: At terminal velocity, speed is constant so weight is in equilibrium with aerodynamic drag.) b) At what speed should the wind tunnel be run in order to achieve dynamic similarity? c) Find the aerodynamic drag force of the model parachute in the wind tunnel in pounds.

(Review experimental scaling) A lightweight parachute is being designed for military use. Its diameter D is 20 ft and the total weight W of the falling payload, parachute, and equipment is 190 lb. The design terminal settling speed V. (or terminal velocity) of the parachute at this weight is 16 ft/'s. A one-twelfth scale model of the parachute is tested in a wind tunnel. The wind tunnel temperature and pressure are the same as those of the prototype, which is 70 °F and standard atmospheric pressure. a) Calculate the drag coefficient of the prototype. (Hint: At terminal velocity, speed is constant so weight is in equilibrium with aerodynamic drag.) b) At what speed should the wind tunnel be run in order to achieve dynamic similarity? c) Find the aerodynamic drag force of the model parachute in the wind tunnel in pounds.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**Design of a Lightweight Parachute for Military Use**

A lightweight parachute is being developed for military applications. Key specifications include:

- **Diameter $ D $:** 20 ft
- **Total weight $ W $:** 190 lb (including payload, parachute, and equipment)
- **Terminal settling speed $ V_t $:** 16 ft/s for the full-scale parachute

A one-twelfth scale model of the parachute is tested in a wind tunnel. The environmental conditions for the test (temperature and pressure) are identical to those for the full-scale prototype, set at 70°F with standard atmospheric pressure.

### Tasks

**a) Calculation of Drag Coefficient**

- Determine the drag coefficient of the prototype with the assumption that at terminal velocity, the weight is balanced with aerodynamic drag.

**b) Wind Tunnel Speed for Dynamic Similarity**

- Establish the wind tunnel speed required to achieve dynamic similarity with the scale model.

**c) Aerodynamic Drag Force on Model**

- Compute the aerodynamic drag force acting on the model parachute within the wind tunnel in pounds.

### Diagram Overview

The provided diagram illustrates the parachute system. It includes the parachute canopy, the payload, and the effective terminal velocity $ V_t $. The diameter $ D $ is indicated at the top of the parachute.

This structured approach to evaluating parachute dynamics ensures accuracy and performance under specified conditions.

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