Aerospace engineering on the back of an envelope / Irwin E. Alber.

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.

Machine converted from AACR2 source record.