IOWA STATE UNIVERSITY - Aerospace Engineering

Course Information

  • Course Title: AER E 1600
  • Lecture Number: 2
  • Instructor: Carolyn Riedel

Units & Significant Figures

SI Units
  • Length
    • Quantity: Length
    • Name: Kilometer, Meter
    • Symbol: km/m
  • Mass
    • Quantity: Mass
    • Name: Kilogram, Gram
    • Symbol: kg/g
  • Time
    • Quantity: Time
    • Name: Second
    • Symbol: s
  • Force
    • Quantity: Force
    • Name: Newton
    • Symbol: N
    • Equivalent Formula: F=m⋅kgs2F = m \cdot \frac{kg}{s^2}
  • Pressure
    • Quantity: Pressure
    • Name: Pascal
    • Symbol: Pa
    • Equivalent Formula: P=Nm2P = \frac{N}{m^2}
  • Temperature
    • Quantity: Temperature
    • Name: Celsius/Kelvin
    • Symbol: C/K
  • Density
    • Symbol: ρ
    • Equivalent Formula: ρ=kgm3\rho = \frac{kg}{m^3}
English Units
  • Length
    • Quantity: Length
    • Name: Mile, Foot, Inch
    • Symbol: mi/ft/in
  • Mass
    • Quantity: Mass
    • Name: Slug
    • Symbol: slug
  • Time
    • Quantity: Time
    • Name: Second
    • Symbol: s
  • Force
    • Quantity: Force
    • Name: Pound force
    • Symbol: lb_f
    • Equivalent Formula: F=ftslug⋅s2F = \frac{ft}{slug \cdot s^2}
  • Pressure
    • Quantity: Pressure
    • Name: Pounds per square inch
    • Symbol: PSI
    • Equivalent Formula: P=lbfin2P = \frac{lb_f}{in^2}
  • Temperature
    • Quantity: Temperature
    • Name: Fahrenheit/Rankine
    • Symbol: F/R
  • Density
    • Symbol: ρ
    • Equivalent Formula: ρ=slugft3\rho = \frac{slug}{ft^3}
Conversion Factors (From Appendix C)
  • 1 ft = 0.3048 m
  • 1 slug = 14.594 kg
  • 1 lb = 4.448 N
  • 1 K = 1.8 °R
  • 1°C=59(°F−32)1 °C = \frac{5}{9} (°F - 32)

Unit Conversion Practice

Converting Feet to Meters
  • Problem: If 1 ft = 0.3048 m, what is 55 ft in meters?
Converting Slugs to Kilograms
  • Problem: If 1 slug = 14.594 kg, how many kilograms is 82.79 slugs?
Converting Pound Force to Slugs
  • Problem: A part weighs 165 lbs. What is the mass of the part?
  • Given: A=32.2  ft/s2A = 32.2 \; ft/s^2

Which Unit System?

  • Engineers working in America will use both SI and English units.
  • Importance: Keep track of the system in use and verify what is reported or given.

Significant Figures

  • Definition: Significant figures are essential for accuracy in reported numbers.
  • Importance: Not enough figures may lead to estimates, while too many can result in inaccuracies.
  • Rule: Report the accuracy of your final number based on the least accurate measurement.
  • Rounding: Round numbers at the final stage to prevent losing detail in calculations.
Significant Figures: A Quick Review
  • Any nonzero number is significant.
    • Example: 1,234 has 4 significant figures.
  • Leading zeros are not significant.
    • Example: 0.00134 has 3 significant figures.
  • Trailing zeros but not behind a decimal are not significant.
    • Example: 12,300 has 3 significant figures.
  • Zeros between significant figures are significant.
    • Example: 12,030 has 4 significant figures.
  • Zeros following a number, to the right of the decimal, are significant.
    • Example: 12,300.0 has 6 significant figures.
Significant Figures: Practice Problems
  1. The maximum velocity of the P-15 Mustang is 438 mph at an altitude of 25,000 ft.
    • Measure velocity to the nearest 1 mph, altitude to the nearest 10 ft.
    • Determine significant figures for both.
  2. The same maximum velocity can be measured to the nearest tenth of a mph and altitude to the nearest 100 ft.
    • Determine significant figures for both.
Significant Figures: Things to Note
  • Known conversion factors are considered perfectly precise, with infinite significant digits.
    • Example: 1 m = 100 cm and 1 ft = 0.3048 m.
  • Constants with multiple decimal places should be noted: use values that maintain at least the precision of the least precise measurement.
    • Example: 9.8 $m/s^2$ vs 9.81 $m/s^2$.

Well Known Unit Conversion Errors

Mars Climate Orbiter
  • Launch Date: December 11, 1998
  • Lost Date: September 23, 1999
  • Error: Missed intended orbit by approximately 60 miles.
  • Cause: Thrust data sent in English units; navigation team expected metric.
Problem: Thrust Miscalculation
  • A solid rocket booster specification required 1.0 ∙ 107 lb of thrust.
  • Question: If this was mistakenly interpreted in Newtons, calculate the error in pounds using the relation of 1 lb_f = 4.5 N.
Tokyo Disneyland Space Mountain
  • Incident Date: January 26, 2004
  • Background: Built from Disney’s master plans using English units.
  • Issue: New axels ordered without verifying units led to a failure (an axel broke, resulting in a derailment).
Problem: Diameter Miscommunication
  • A bolt was ordered with a thread diameter of 1.25 inches.
  • Questions: What is this diameter in millimeters? If mistakenly read as 1.25 centimeters, by how many millimeters would it be in error?
    • Use the conversions 1 in = 2.54 cm and 1 cm = 10 mm.
Air Canada Flight 143
  • Incident Date: July 23, 1983
  • Description: Flight 143 ran out of fuel due to conversion error in fuel mass.
  • Requirement: Crew needed 22,300 kg of fuel but undercalculated due to incorrect conversion factors.
  • Result: Emergency landing on an old military air force base; no casualties occurred.
Problem: Fuel Calculation
  • Flight 143 needs 22,300 kg of fuel and has 7,682 L already in tank.
  • A. Calculate additional fuel needed using 0.803 kg/L.
  • B. Determine deficiency from the requirement based on a mistaken conversion factor of 1.77.

Summary

  • Importance of units: Accurate units are critical in engineering applications.
  • Significant figures: Highlight the precision of measurements and calculations.

References

  • Newman, Dava. “Chapter 2: Introduction to Engineering.” Interactive Aerospace Engineering and Design, McGraw Hill, New York, NY, 2002, pp. 20–35.
  • Additional images and resources:
    • Space shuttle Columbia Launch Photo (NASA)
    • Mars Climate Orbiter Image (NASA/JPL-Caltech)
    • Tokyo Disneyland Space Mountain Image (Disney Parks Wiki)
    • Canadian Airlines Flight 143 Incident Reference.