Division of Engineering
Brown University
2.4 Estimation
Finally, we discuss estimation in engineering. You will need to make estimates in a wide variety of situations, including:
EN3: Introduction to Engineering and Statics
Division of Engineering
Brown University
2.4 Estimation
Finally, we discuss estimation in engineering. You will need to make estimates in a wide variety of situations, including:
Planning: Estimate the time it will take to complete
a civil engineering project (put up a bridge, dig a tunnel, put up a building);
Estimate the cost of the Big Dig (you can probably do a better job than
the construction managers did)
Evaluating the reliability of data or reports: You’ll
spend a lot of time listning to sales pitches. To separate fact from fiction
you will have to make your own independent estimates of key performance
indicators.
Checking the reliability of your experiments or calculations:
Suppose you’ve developed a sensor to measure stresses in human bones
in situ. Your equipment gives a reading of 
. Is this reasonable?
Suppose your calculations suggest that it will take you 72000 seconds to
fly from New York to Boston. Did you screw up somewhere?
Failure Analysis: Given skid marks on the road at
the scene of an accident, estimate the speeds of the cars involved.
Design parameters: Estimate the reaction time of
a (sober) car driver. Estimate the maximum force that the brake pedal of
your car must withstand during operation. Estimate the greatest wind load
acting on the side of a skyscraper. Estimate the heat dissipated
from an integrated circuit.
Interview questions: Estimation problems are favorites
with job interviewers. Examples: Estimate the number of Big Macs consumed
in the USA per year; estimate the volume of water flushed daily by US households…
Making an estimate is more than just a guess: it is a systematic approximation based on experience and as much data collection as time permits. The more data that is collected, the better the estimate, but the more time, effort and cost that must be expended.
To develop, and present an estimate, you should use the following procedure
The trick to getting a good estimate is to re-define your problem in terms of quantities you feel you can accurately estimate from your past experience. For example, to estimate the annual consumption of Big Macs, you might estimate how many Big Macs you consumed last year, and then scale it by the population of the USA. (In my case, this procedure gives zero. ).
EXAMPLES:
1. Estimate the height of the Sciences Library
Solution:
Problem: To estimate the height of the Sciences Library
Assumptions or Data Collected
The library has 14 stories, excluding the basement
All floors except 1st are equal in height
Height of 1st floor approx 20ft; height of any other floor
approx 12ft
Space between two floors approx 1.5 foot
Calculations: Total height =
ft
Error:
Error in height of any floor approx 2 ft
Error in total height approx 28ft or 14%.
To improve estimate
Borrow Division’s Total Station and survey the building;
ask a librarian.
Notice that we decided to do this problem using units of ft. When making an estimate, it is helpful to work with units that make the best sense to you. You can always convert later.
2. Estimate the contact pressure (force per unit area) under an average person’s feet; under a passenger car tire; and under a two wheel bicycle, and one of the ball bearings supporting the axle of your car.
Solution:
The Problem: Estimate the contact pressure (force per unit area) under an average person’s feet; under a passenger car tire; under a two wheel bicycle, and one of the ball bearings supporting the axle of your car.
Assumptions and Data
Average mass of a person: approx 100 kg
Average mass of a car: 1500 kg
Approx mass of a bicycle: 6 kg
Approx force on a ball bearing: weight of car/4 shared by
5 balls = 
where the 9.81 is the acceleration due to gravity.
Contact area of a foot: each foot makes contact over two
areas; measuring about 2 inches by 1.5 inches. Total is 
Contact area of car tires: 4 contacts, equally loaded, at
about 
so total is about =
total
Contact area of bike tires: 2 contacts, equally loaded at
about 
=
Contact area of ball bearing: contact area is roughly circular,
perhaps 0.1mm radius, so area is about 
Calculations:
Person: pressure =force/area = 
Car pressure =force/area = 
Bike pressure =force/area = 
Ball bearing: force/area = 
Wow!
Error estimate:
Person’s weight: +/- 20kg
Car’s weight: +/- 500 kg
Bike’s weight +/- 3kg
Bearing force +/- 30%
Contact area of foot: +/- 20%
Contact area of car and bike tire: +/- 20%
Contact area of ball bearing: +/- 50%
Totals
Foot pressure: +/- 40% (adding the percentage errors –
this is a bit pessimistic)
Car +/- 50%
Bike +/- 40%
Ball bearing +/- 70%.
To improve estimate
Measure weights accurately – get a large sample of
people and take an average; consult manufacturers data for vehicle weights.
Contact areas could be measured – carbon paper between two sheets
of paper would work well for foot, car & bike tire. Ball bearing is
tough – best approach here is to calculate contact area theoretically.
Example 3: You are conducting a feasibility study for a consortium of wealthy developers who wish to construct the Mall of the Universe in Massachusetts.
The mall will naturally require a parking lot, which is to be located in Rhode Island. In fact, R.I will be the parking lot. Estimate:
Solution
Assumptions and Data
Idealize RI as rectangular, with dimension 
square miles
(see map). Total area is therefore approx 
Assume that cars are parked as shown in the figure below
With this scheme each parking space needs a total of 
associated with
it (you need 2m by 3m of travel lane per spot). Data source: measurements
at 3 parking lots.
Cost per space in a parking lot is approx $1500 (International
Parking Institute)
U.S. Population is 270 million. (www.census.gov/main/www/popclock.html)
Assume 1 car for every three people
Calculation
No. parking spots = area of RI/area per spot = 
cars.
Cost: 
- that’s 150 billion dollars – even Bill Gates
($36 billion) couldn’t afford it…
Total no. cars required to accommodate all US is approx
90 million. We predict that they would just fit.
Error estimate:
Area of state: +/- 20%
Space per parking lot: +/- 5%.
Paving cost +/- 50%
No. cars in US +/- 20%
Error in no. parking spaces +/- 25%; cost 70%.
To improve estimate:
Obtain accurate survey data; lay out parking spaces explicitly
Get quotes per parking space from paving companies (see
if you can get a good deal for such a big order)
Buy recent census data for no. cars.
Exercises: (To be discussed in class, section, or for self-study)
