TY  - BOOK
AU  - Alber,Irwin E.
TI  - Aerospace engineering on the back of an envelope
T2  - Springer-Praxis books in astronautical engineering
SN  - 3642225365
AV  - TL545 .A43 2012
U1  - 629.1 23
PY  - 2012///
CY  - Heidelberg, Chichester, UK
PB  - Springer, Published in association with Praxis Publishing
KW  - Aerospace engineering
KW  - Engineering design
N1  - Includes bibliographical references and index; 1. Introduction -- 2. Design of a high school science-fair electro-mechanical robot -- 3. Estimating Shuttle launch, orbit, and payload magnitudes -- 4. Columbia Shuttle accident analysis with Back-of-the-Envelope methods -- 5. Estimating the Orbiter reentry trajectory and the associated peak heating rates -- 6. Estimating the dimensions and performance of the Hubble Space Telescope -- --; 1; Introduction --; 1.1; Why Back-of-the-Envelope engineering? --; 1.1.1; Back-of-the-Envelope engineering; an important adaptation and survival skill for students and practicing engineers --; 1.1.2; Design of a high school science fair electro-mechanical robot --; 1.1.3; Design of a new commercial rocket launch vehicle for a senior engineering student's design project --; 1.1.4; Preliminary design of a new telescope system by an engineer transferred to a new optical project --; 1.1.5; Examining the principles and ideas behind Back-of-the- Envelope estimation --; 1.2; What is a Back-of-the-Envelope engineering estimate? --; 1.2.1; Tradeoffbetween complexity and accuracy --; 1.2.2; Back-of-the-Envelope reasoning --; 1.2.3; Fermi problems --; 1.2.4; An engineering Fermi problem --; 1.3; General guidelines for building a good engineering model --; 1.3.1; Step by step towards estimation --; 1.3.2; Quick-Fire estimates --; 1.4; Quick-Fire estimate of cargo mass delivered to orbit by the Space Shuttle --; 1.4.1; Cargo mass problem definition --; 1.4.2; Level-0 estimate: the empirical ''rule of thumb'' model --; 1.4.3; Level-1 estimate: cargo mass using a single stage mathematical model based on the ideal rocket velocity equation --; 1.4.4; Level-2 estimate: cargo mass using a two stage vehicle model based on the ideal rocket velocity equation --; 1.4.5; Level-3 estimate: cargo mass delivered by a two stage vehicle; based on a revised estimate for second stage structural mass fraction --; 1.4.6; Impact of added knowledge and degree of model complexity --; 1.4.7; Moving from the Shuttle to the Hubble Space Telescope --; 1.5; Estimating the size of the optical system for the Hubble Space Telescope --; 1.5.1; System requirements for the HST --; 1.5.2; Shuttle constraint on HST size --; 1.5.3; Estimating the length of the HST optical package --; 1.6; Concluding remarks --; 1.7; Outline of this book --; 1.8; References --; 2; Design of a high school science-fair electro-mechanical robot --; 2.1; The Robot-Kicker Science Fair Project --; 2.2; Back-of-the-Envelope model and analysis for a solenoid kicking device --; 2.2.1; Defining basic dimensions and required soccer ball velocity --; 2.2.2; Setting up a Bot Emodel for the solenoid kicking soccer ball problem --; 2.2.3; Model for solenoid kicker work and force --; 2.2.4; Final design requirements for linear-actuator solenoid and supporting electrical system --; 2.3; Appendix: Modeling of the temperature rise produced by ohmic heating from single or multiple solenoid-actuator kicks --; 2.3.1; Quick-Fire problem approach --; 2.3.2; Problem definition and sketch --; 2.3.3; The baseline mathematical model --; 2.3.4; Physical parameters and data --; 2.3.5; Numerical results --; 2.3.6; Interpretation of results --; 2.4; References --; 3; Estimating Shuttle launch, orbit, and payload magnitudes --; 3.1; Introduction --; 3.1.1; Early Space Shuttle goals and the design phase --; 3.1.2; The Shuttle testing philosophy and the need for modeling --; 3.1.3; Back-of-the-Envelope analysis of Shuttle launch, orbit, and payload magnitudes --; 3.2; Shuttle launch, orbit, and reentry basics --; 3.2.1; The liftoffto orbit sequence --; 3.2.2; Reentry --; 3.3; Inventory of the Shuttle's mass and thrust as input to the calculation of burnout velocity --; 3.3.1; Burnout velocity --; 3.3.2; The velocity budget --; 3.3.3; Mass inventory --; 3.3.4; Thrust and specific impulse inventory --; 3.4; Mass fraction rules of thumb --; 3.5; Quick-Fire modeling of the takeoffmass components and takeoffthrust using SMAD rules of thumb --; 3.5.1; Quick-Fire problem approach --; 3.5.2; Problem definition and sketch --; 3.5.3; Mathematical/''Rule of Thumb'' empirical models --; 3.5.4; Physical parameters and data --; 3.5.5; Numerical calculation of total takeoffmass, cargo bay mass, and total takeoffthrust --; 3.5.6; Interpretation of the Quick-Fire results --; 3.5.7; From Quick-Fire estimates to Shuttle solutions using more accurate inputs --; 3.6; Ideal velocity change Dv for each stage of an ideal rocket system --; 3.6.1; Propellant mass versus time --; 3.6.2; Time varying velocity change --; 3.6.3; Effective burnout time and average flow rate --; 3.6.4; Ideal altitude or height for each rocket stage --; 3.7; Dvideal estimate for Shuttle first stage, without gravity loss --; 3.7.1; Estimate of SSME propellant mass burned during first stage --; 3.7.2; First stage mass ratio and average effective exhaust velocity --; 3.7.3; Average specific impulse for the ''parallel'' (solidþliquid) first stage burn --; 3.7.4; Dvideal estimate for Shuttle first stage --; 3.7.5; Dvideal and altitude as functions of time, for the Shuttle first stage --; 3.8; The effect of gravity on velocity during first stage flight --; 3.8.1; Modeling the effects of gravity for a curved flight trajectory --; 3.8.2; Time-varying pitch angle model --; 3.8.3; Effect of gravity on rocket velocity during first stage flight --; 3.8.4; Effect of gravity on rocket height during first stage flight --; 3.8.5; Comparing model velocity and altitude with Shuttle data --; 3.8.6; Gravity loss magnitudes for previously flown launch systems --; 3.8.7; Model velocity, with gravity loss, compared with flight data --; 3.8.8; Calculation of gravity-loss corrected velocity at first stage burnout --; 3.9; The effect of drag on Shuttle velocity at end of first stage flight --; 3.9.1; Modeling the effects of drag in the equation of motion --; 3.9.2; Estimating first stage drag loss --; 3.9.3; Final drag and gravity-corrected velocity at first stage burnout; key elements of the overall ''velocity budget'' for the first stage --; 3.10; Calculation of second stage velocities and gravity losses --; 3.10.1; Pitch and gravity loss modeling for the second stage flight period --; 3.10.2; Time-varying gravity loss solution, region 2a --; 3.10.3; Time-varying velocity solution, region 2b --; 3.10.4; Combined velocity solution for regions1, 2a, and 2b and v(MECO) --; 3.11; Summary of predicted Dv budget for the Shuttle --; 3.12; Comparison of Back-of-the-Envelope modeled Shuttle velocity and altitude as a function of time to NASA's numerical prediction for all stages --; 3.12.1; Comparison of model velocity with NASA's numerical prediction --; 3.12.2; Comparison of model altitude with NASA's numerical prediction --; 3.12.3; Modeled altitude sensitivity to pitch time scale --; 3.13; Estimating mission orbital velocity requirements for the Shuttle --; 3.13.1; Part1: circular orbital velocity --; 3.13.2; Part2: elliptical orbits and the Hohmann transfer Dv's --; 3.13.3; Numerical values for transfer orbit Dv's --; 3.13.4; Time of flight for a Hohmann transfer --; 3.13.5; Direct insertion to a final orbital altitude (without using a parking orbit) --; 3.14; A Back-of-the-Envelope model to determine Shuttle payload as a function of orbit altitude --; 3.14.1; Analytic model for payload as a function of orbital altitude --; 3.14.2; Approximate linearized solution for payload --; 3.14.3; Reduction in useful cargo mass due to increases in OMS propellant mass --; 3.14.4; OMS models for correcting cargo or payload mass --; 3.14.5; Model for rate of change of ''useful cargo'' with altitude --; 3.14.6; Approximate analytic model for useful cargo --; 3.14.7; Modeling missions to the International Space Station --; 3.15; Tabulated summary of Back-of-the-Envelope equations and numerical results --; 3.16; References --; 4; Columbia Shuttle accident analysis with Back-of-the-Envelope methods --; 4.1; The Columbia accident and Back-of-the-Envelope analysis --; 4.1.1; Bot Emodeling goals for the Columbia accident --; 4.1.2; Quick estimation vs accurate estimation --; 4.2; Quick-Fire modeling of the impact velocity of a piece of foam striking the Orbiter wing --; 4.2.1; Interpretation of Quick-Fire results --; 4.2.2; The bridge to more accurate Bot Eresults --; 4.3; Modeling the impact velocity of a piece of foam debris relative to the Orbiter wing; estimations beyond the Quick-Fire time results --; 4.3.1; Looking at the collision from an earth-fixed or moving Shuttle coordinate system --; 4.3.2; The constant drag approximation --; 4.3.3; Analytically solving for the impact velocity and mass, given the time to impact --; 4.3.4; Summary of results for constant acceleration model compared to data --; 4.3.5; The non-constant acceleration solution --; 4.3.6; An estimate of impact velocity and particle mass, taking the time to impact as given (the ''inverse'' problem) --; 4.3.7; Comparing Osheroff 's ''inverse'' calculations to our ''direct'' estimate results --; 4.3.8; Concluding thoughts on the impact velocity estimate --; 4.4; Modeling the impact pressure and load caused by impact of foam debris with an RCC wing panel --; 4.4.1; The impact load --; 4.4.2; Impact overview --; 4.4.3; Impact load mathematical modeling --; 4.4.4; Elastic model for the impact stress --; 4.4.5; Elastic-plastic impact of a one-dimensional rod against a rigid-wall --; 4.4.6; The elastic-plastic model --; 4.4.7; Numerical results and plotted trends --; 4.4.8; Impact area estimate --; 4.4.9; Load estimate --; 4.4.10; Impact loading time scale (Bot E) --; 4.4.11; Loading time histories, numerical simulations --; 4.5; Develop a Back-of-the-Envelope engineering stress equation for the maximum stress in the RCC panel face for a given panel load --; 4.5.1; Bot Epanel stress model --; 4.5.2; Estimates for the allowable maximum stress or critical load parameters for failure --; 4.5.3; Final comments on the prediction of possible wing damage or failure --; 4.6; Summary of results for Sections 4.2, 4.3, and 4.4 --; 4.7; References --; 5; Estimating the Orbiter reentry trajectory and the associated peak heating rates --; 5.1; Introduction --; 5.2; The deorbit and reentry sequence --; 5.3; Using Quick-Fire methods to crudely estimate peak heating rate and total heat loads from the initial Orbiter kinetic energy --; 5.3.1; Quick-Fire problem definition and sketch --; 5.3.2; The Quick-Fire baseline mathematical model, initial results, and interpretation --; 5.4; Alook at heat flux prediction levels based on an analytical model for blunt-body heating --; 5.4.1; Numerical estimates of Stanton number using the Sutton- Graves constant --; 5.5; Simple flight trajectory model --; 5.5.1; Asimple Bot Emodel for the initial entry period; the entry solution --; 5.5.2; The equilibrium glide model --; 5.6; Calculating heat transfer rates in the peak heating region --; 5.6.1; Selecting the nose radius --; 5.6.2; Comparing the model maximum rate of heat transfer, q_wmax , with data --; 5.6.3; Model estimate for nose radiation equilibrium temperature, Tmax --; 5.6.4; Model calculations of q_w as a function of time --; 5.6.5; Model calculations for total heat load at the stagnation point --; 5.7; Appendix: Bot Emodeling of non-Orbiter entry problems --; 5.8; References --; 6; Estimating the dimensions and performance of the Hubble Space Telescope --; 6.1; The Hubble Space Telescope --; 6.1.1; HST system requirements --; 6.1.2; HST engineering systems --; 6.1.3; Requirements for fitting the HST into the Orbiter --; 6.2; The HST Optical Telescope design --; 6.2.1; The equivalent system focal length --; 6.2.2; How do designers determine the required system focal ratio, Feq? --; 6.2.3; Telescope plate scale --; 6.2.4; Selection of HST's primary mirror focal ratio, F 1 1/4 jf1j=D --; 6.2.5; Calculating the magnification m and exact constructional length L --; 6.2.6; Estimating the secondary mirror diameter --; 6.2.7; Estimating the radius of curvature of the HST secondary mirror --; 6.3; Modeling the HST length --; 6.3.1; The light-shield baffle extension --; 6.3.2; Modeling the length of the light shield --; 6.3.3; The length of the instrument section --; 6.3.4; Calculating the total HST telescope length --; 6.4; Summary of calculated HST dimensions --; 6.5; Estimating HST mass --; 6.5.1; Primary mirror design --; 6.5.2; Estimating primary mirror mass --; 6.5.3; The estimated total HST system mass and areal density --; 6.5.4; Some final words on the HST mass estimation exercise --; 6.5.5; Onward to an estimate of HST's sensitivity --; 6.6; Back-of-the-Envelope modeling of the HST's sensitivity or signal to noise ratio --; 6.6.1; Defining signal to noise ratio --; 6.6.2; Modeling the mean signal, S --; 6.6.3; Modeling the noise --; 6.6.4; Final equation for signal to noise ratio --; 6.6.5; Final thoughts on Bot Eestimates for HST sensitivity --; 6.7; References
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