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NASA-Threads
Work and Mechanics
Lesson 24: Efficiency
Definition of Efficiency
The efficiency of a system is the ratio of the useful energy output of the system to the
required energy input to the system.
𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 = 𝜼 =
𝒖𝒔𝒆𝒇𝒖𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒐𝒖𝒕𝒑𝒖𝒕
∙ 𝟏𝟎𝟎%
𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒆𝒏𝒆𝒓𝒈𝒚 𝒊𝒏𝒑𝒖𝒕
For the servo, the efficiency is . . .
𝜼=
𝑷𝑬 𝒄𝒉𝒂𝒏𝒈𝒆 𝒐𝒇 𝒘𝒆𝒊𝒈𝒉𝒕
∙ 𝟏𝟎𝟎%
𝒆𝒍𝒆𝒄𝒕𝒓𝒊𝒄𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒑𝒓𝒐𝒗𝒊𝒅𝒆𝒅 𝒕𝒐 𝒔𝒆𝒓𝒗𝒐
𝑊𝑡 ∙ ∆ℎ
𝜂=
∙ 100%
𝑉∙𝐼∙𝑡
Let’s look at the units:
Wt
= weight (N)
∆h
V
= change in height of weight (m)
= voltage to servo (V)
I
t
= current drawn by servo (A)
= time that servo is operated (s)
NASA-Threads
Work and Mechanics
Lesson 24: Efficiency
Examples
CLASS PROBLEM: Assume the data below was collected during your servo
efficiency project. Compute the resulting servo efficiency.
CLASS PROBLEM: A crawler-transporter is used to transport the Space Shuttle
from NASA’s Vehicle Assembly Building (VAB) to Launch Complex 39. The crawler
weighs 5,400,000 lbs and the Space Shuttle liftoff weight is 4,400,000 lbs, which
includes the Space Shuttle, payload, external fuel tank, and solid rocket boosters.
As the crawler approaches the launch pad, it travels up a 5% grade ramp to the
launch pad for a total elevation change of 12 meters.
(a) What is the potential energy change of the Crawler/Shuttle system as it
climbs the ramp? Please use SI units.
(b) If the diesel engines and the gearing system that drives the crawler have a
combined efficiency of 20%, then how much chemical energy (due to
combustion) must be provided by the diesel fuel used to run the engines?
NASA-Threads
Work and Mechanics
Lesson 24: Efficiency
CLASS PROBLEM: You’ve always dreamed of doing something “special” with your
life that others would notice. So, you decide that it would be really cool to build a
structure at the top of Mt. Everest out of the smooth stones collected at the mouth
of a small stream flowing into the ocean. Because of your love for the science and
the space program, you decide that it would be symbolic if the potential energy
change of the rocks that you carried to the top of Mt. Everest roughly added up to
the same potential energy change of the Crawler / Shuttle system as it climbed up
to Launch Pad 39A (9,800,000 lbs. being elevated 12 meters).
How many backpacking trips will it take you to accomplish your goal if you can pack
25 lbs. of rocks in addition to the basic supplies required for survival?