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ESTIMATION
Lecture Notes
12/1/96
by W. Durfee
(Acknowledgments to my good friend Woodie Flowers of MIT who is responsible for the original idea, the format and much of the content of this lecture.)
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(bring notebook, physics text, 20# toolbox, string, scissors, crushable calculator, quiz)
(Pass out quiz at start -- no peeking)
Order:
Overview
Quiz
More overview
Observation
Models
Measurements
Calculation
Concluding remarks
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OPENING MATERIAL
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ESTIMATION = quick models + quick measurements + quick calculations.
Vital for rapid concept generation, concept selection.
Important part of evaluating ideas ---- RAPID IS THE KEY.
One of your MOST IMPORTANT ENGINEERING TOOLS -- pay attention.
AS A DESIGNER:Estimation <---> Builds strong intuitive knowledge
Estimation <---> Sanity check on detailed design
AS A MANAGER:Estimation <---> ability to ask correct questions and determine whether answer makes sense
Example: At a recent mid-quarter design review student said "This structure will resonate at 10KHz", talking about an 8' high stand to hold some scientific equipment at roadside. EXPERIENCED ENGINEERS IN THE AUDIENCE KNEW IT DIDN'T MAKE SENSE AND CALLED THE STUDENT ON IT. Student responded, "Well, my original calculations said 100KHz and I knew that was wrong so I redid the calculations and came out with 10KHz". Clearly, student did not have good sense of ESTIMATION.
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QUIZ
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OK, let's do an estimation quiz. You won't hand it in. You have 8 minutes. Go.
(do the quiz)
Exchange your quiz with the person behind you. Take 2 minutes to look over their answer. Take another 3 minutes to discuss the quiz using the questions below.
(pair or trio discussion)
CLASS DISCUSSION:
Why was this a hard quiz?
What info would you have liked to have had?
(assumptions, calculations)
HERE ARE SOME "ANSWERS":
1. What fan flow rate is required in the HVAC system to turn over the air four times each hour in this room?
(for ME 18)
APPROX ANS: 25 x 50 = 1250, x 10 = 12500 cf. Need to move this many cubic feet every 15 minutes.
12500 cf / 15 min == 1000 cfm fan
EXACT ANS: Room is 24' by 54' by 9' = 11,664 cubic ft. Need
11664 cf / 15 min = 778 cfm fan. (This is a small fan. A 30" whole house attic fan is 6000 cfm).
2. How many stress cycles does an average automobile tire go through each year?
ANS: Assume 10K mi per year for car. Tire is 24" dia, circum is
24 x 3 = 72 in = 6 ft. Tire travels 10000 mi x 5280 ft/mi =
10x10E3 x 5.2x10E3 = 52x10E6 ft.
Revolutions = 52x10E6 ft / 6 ft/rev = 9x10E6 = 9 million cycles!
3. How high can you be lifted by the energy in a 9v battery?
ANS: Estimate 9v batt can put out 1 Amp for 30 minutes = 9 Watts for 0.5 hrs ==> 4.5 watt-hrs. (or can estimate by considering how long it could light a 1 W flashlight bulb, or can look at the data sheet which says 5 watt-hrs).
(4.5 W-hrs / 746 W/hp) x 550 (ft-lb/sec)/hp = 3.3 (ft-lb/sec)-hrs.
3.3 x 3600 sec/hrs = 11880 ft-lbs.
For 160 lb. person ---> 11880/160 = 75 ft!
MORE OVERVIEW
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THE KEY IS TO KEEP THINGS SIMPLE...... VERY SIMPLE
- Remember the goal: rough cut, sanity check, general feasibility.
- You are not using estimation for the same purposes that you would an FEM code.
- You are not using estimation for design optimization.
- You are using it to test concepts.
- You are using it on-line to check someone else's design that you are hearing for the first time in a design team meeting, or as a manager in a design review.
YOU SHOULD ESTIMATE ALL THE TIME:
WHILE YOU WALK (volume/weight of concrete per sidewalk
slab?),
WHILE YOU DRIVE (area of overhead highway sign),
WHILE YOU EAT (how strong does a fork have to be?),
WHILE YOU ARE SITTING IN LECTURE (how much longer is this
going to go on?)
EXAMPLE: What does a 5 g pail of liquid weigh. (55g drums are out, 5g pails are in -- safety, ease of storage, ease of transport)
Density of water: 1000 kg/m3 or 1.0 gm/cm3 or more simply....
1.0 kg/liter or 1 pound/pint
How far off are we on “a pint’s a pound” ?
1 gal = 231 in3 = 3.79 liters ==> 3.79 kg (x 2.2.05 lb/kg) =
8.347 lbs
1 gal = 8 pints ==> 1 pint weighs 8.347/8 = 1.043 lbs
(“pint’s a pound” is off by 4%)
Call 1 gal (= 8 pints) 8 lbs
5 gal is 40 lbs (exact is 41.74 lbs, 4% error)
OR..... water is 1 kg/liter == 2.2 lbs/qt = 8.8 lbs/gal
==> 5 gal weighs about 9 x 5 = 45 lbs. (8% error)
Convenient since OSHA limit is 50 lbs.
FOUR COMPONENTS TO THE ESTIMATION PROCESS
1. Observe
2. Model
3. Measure or recall
4. Calculate
You should develop facility in all four.
1. OBSERVATION
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Good estimation is tied to good observation. NOTICE WHAT IS AROUND YOU. CALIBRATE WHAT IS AROUND YOU. Take some time now and
notice the room around you.
EXERCISE: Now close you eyes. What is:
Color of my shirt?
Describe the texture of the walls.
Number and type of light fixtures in the room?
Are there exit signs? How many?
Color of door?
Number of seats in a row?
Support structure for your chair?
OK, open up and look around.
As engineers, you are obligated to be observing at all times.
-- Notice the chairs (size, material ==> intuitive feel for strength)
-- Notice a coke can (material, wall thickness, how the top is assembled)
-- Notice a staple (how it’s formed during stapling, what happens when it jams)
2. MODELS
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The key here is to KEEP IT SIMPLE, VERY SIMPLE:
- uniform acceleration
x = (1/2)at2 (start from rest)
- 2nd order vibrations (spring-mass)
W^2 = K/M
- axial tension/compression of a beam (dX = PL/AE)
(P=load, A=area, E=young’s modulus)
- deflection of cantilever beams (dX = PL^3/3EI)
I = bh^3/12 for rectangluar beams
(h = load carrying direct.)
- pin-pin beams (dX = PL^3/48EI)
For slender beams, pin-pin is good assumption
- 1-D heat transfer
- etc...... (form your own collection)
Anything more complex usual requires the reference book. We are looking for order-of-magnitude only.
3. MEASUREMENTS
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Because you need to put numbers in your model. Separates the doers from the thinkers
The key is to DEVELOP A SET OF CALIBRATIONS OVER A WIDE RANGE.
Low extreme --- Middle range (human experience) --- High extreme
For "human range", use body centered measuring tools (examples below).
LENGTH
0.5 micron (modern IC feature)
70 micron (human hair) (.003")
.004 (paper thickness)
1 in(quarter) (actual = a little over 15/16")
6 in(dollar) (actual = 6 3/32")
9 in(my finger span)
1 ft (standard floor tile)
6 ft(my outstretched arms)
100 m(football field)
1 mi(4 times around the track, 1 min in a car)
240,000 mi (distance to moon)
92 million mi (distance to sun)
TIME
1 ns(time it takes light to travel a foot)
100 ms(human reaction time)
0.5 s(4 ft drop of an object)
1 s("a-thousand-one-a-thousand-two.....")
minutes, hours, days, years(you know these)
FREQUENCY
Closely related to time. Count it
4 Hz(beat your hand, 4 to the bar!)
440 Hz(Concert A on the piano)
1 KHz(high for a mechanical resonance)
10 MHz(Digital IC speeds)
VELOCITY
1 fps(follow with your finger)
60 mph(a car of course)
200 mph(airplane taking off)
3E8 m/s(speed of light)
ACCELERATION
1.0 g 9.8 m/s2 32.2 ft/s2
2.7/T (g's for car in 0-60 mph test,
0.27 g's for 10 seconds)
9.1/T (g's for airplane 0-200 mph test
0.6 g's for 15 seconds)
6 g's 30-0 mph in 5 ft (1/4 sec) crash
200 g's(any object, 4 ft drop test onto hard surface with
0.25 in. crush zone for deceleraltion)
(0.5 s fall time, 16 ft/s at impact,
2.5 ms crush time)
Use your body to sense/guess: Example: what’s the g’s for
an elevator?
FORCE/WEIGHT
1 oz (4 quarters? Measure it (weigh a roll))
1 lb(box of nails, tub of coleslaw, pint of water)
10 lbs(big bag of flour)
25 lbs(bag of dog food)
xxx lbs(body weight)
1 ton(a car)
????(big trucks)
????(airplane, ships)
TORQUE
1 ft-lb(imagine a 12" bar with a one lb weight)
200 ft-lbs (me hanging off a 15" bar)
PRESSURE
9 psi (playground ball)
4.3 psi (10 ft. column of water)
or, water is 1/2 psi per foot.
14.7 psi(ground level air pressure)
100 psi(standard pneumatic automation)
5000 psi(very high pressure hydraulics)
EXAMPLE: What’s the pressure at your outdoor tap? Hose can shoot 30 ft into the air. Water is 1/2 psi per foot, so 60 psi at nozzle. But, assume shooting process is 50% efficient, so 30 psi at nozzle.
POWER
1 W(flashlight bulb)
100 W(bright house bulb)
10,000 W(movie lamp)
200 Hp(big car engine)
ENERGY
ELASTICITY
10E6 psi(E for aluminum)
30E6 psi(E for steel)
TENSILE STRESS
100,000big number for steel
30,000big number for aluminum
TEMPERATURE
32 Fwater freezes
212 Fwater boils
ETC...... develop your own set.....WHATEVER WORKS
MEMORIZE AS MANY OF THESE AS YOU CAN. The more you have at your rapid disposal, the better you will be at estimation. (Or, carry around a crib sheet.) This is where you will calibrate yourself on what's a big number, what's a small number and what's a reasonable number.
4. CALCULATIONS
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CALCULATORS
Calculators are the enemy of rapid estimation.
If you need a calculator, you are probably using too much precision for R.E.
Calculators are too slow for R.E. Have you ever been at a meeting....”Oh, I’ll just do this on my calculator...” and you had to wait forever to get the answer.
Too easy to make an order-of-magnitude mistake with calculators.
Here's what we think of them...
(Do the calculator crush. A toolbox with 20# of scrap metal hanging by a string from my hand directly over the calculator. Have three students estimate the weight. Cut the string. **Crunch!!** Open the toolbox. Inside is a pencil.)
How much energy was in that collision?
(20 lbs x 1 ft = 20 ft-lbs)
Two parts to R.E. calculations: (1) Roundoff, (2) Conversions
ROUNDOFF
Remember, looking for order of magnitude only!
8 == 10, 23 == 20, 32.2 fpss == 30, Pi == 3
Use factors of 10 whenever possible (easy to mul, div)
Mental computation excellent for checking precision
calculations as well (e.g., am I off by 100 when
I pressed the calculator buttons?)
CONVERSIONS
My frosh physics text is well worn, not because I am
wondering about Planck's constant, but because it has
a great set of conversion tables.
(I took frosh Physics in '72-'73....estimate my age)
Try to keep a collection of useful ones in your head.
I write down all domain related ones on the back page
of my design notebook. (Because my memory is lacking)
Can remember at a useful point on the scale
60 mph = 88 fps
1/2 psi == 1 ft of water
Examples of some useful conversions:
25 microns = 1 thou
1 mph = 1.47 fps
1 atm = 14.7 psi = 760 mmHg
1 g = 32.2 fpss
1 BTU = 778 ft-lb
1 hp = 550 ft-lb/s = 746 watts
1 lb = 4.4 Newtons
The best way we could improve our rapid estimation computation skills is for the U.S. to convert to metric!!
If you don’t know the units, you are out of the discussion.
EXAMPLE: Someone says, “The pressure needed to promote skin breakdown is 100 mmHg” and you have no idea what that unit is, you’re in trouble. But, if you can say to yourself, “Hmmm, 100 mmHg is about 1/8 atm or 2 psi or 2 tubs of coleslaw on a 1 in. by 1 in. peg”, you’ve got a much better feel for what’s going on if it is your task to design a pressure relief system.
CLOSING REMARKS
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Start building your personal library. Amaze you friends, impress your boss.
Give yourself estimation problems all the time:
What's the weight of that building?
What's the stress at the root of that airplane wing?
If you can't estimate "on the fly", look it up when you get home.
You will soon be good at saying "Gee, that just doesn't sound right", when assessing concepts.
Good exercise for your engineering brain.
Start to memorize some of the measurements/conversions. The engineering equivalent of anatomy.
The good designer/manager is one who in addition can generate, select and evaluate concepts on the fly.
Edison: Asked 2 interns to find the volume of a light bulb. One computed via integrals, the other filled it with water and then measured the volume of the water.
During job interviews for HP, they will ask you estimation questions.
Any well-trained engineer can do the detailed calculations. You will have lots of competition for that job and as you get older, the young engineers will probably be able to do it better. In fact, most detailed calculations are done by the computer. If all you know how to do is the detail calculations, start scanning the job pages now.
EXAMPLES (**** need lots more)
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1. CANOE LIFT
The battery energy question on the quiz. Not so far fetched. Can you build a motorized version of the car-top canoe lift using a battery power source?
canoe 50-100 lbs. Car top 5 ft ----> Need 500 ft-lbs. 9v battery has 13,270 ft lbs. Can lift 26 times.
But... include efficiency of motor, machinery. Call it 50%. Down to 13 times.
But... want NiCads. Have 30% capacity of alkaline ---> down to 4 lifts with a 9v rechargeable battery.
On a car would probably use the existing 12v source. Ask yourself, how much of an energy/power draw compared to other accessories?
2. CANOE LIFT
Lifting it up beside the car using block and tackle. Cantilever supports that stick out 2 ft.
load = 100 lbs, deflection = PL^3/3EI
aluminum: E = 10E6 psi, L == 20 in, P = 100 lbs
say 1 in by 1 in alum bar ----> E = 1/12 == 0.1
deflection = (100 8000 / 3 10E6 0.1) == 0.3 in
Weight of structure??
3. FAN MISMATCH
In prior quarter of ME 5254, students bought great big fan and an itty-bitty motor. Clearly an estimation mismatch!
EXERCISES
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(****** need to add some******)
1. Estimate volume of water flow in the Mississippi under the Wash Av. bridge.
2. Estimate the weight of the stainless steel skin on the Weisman museum.
3. Estimate the pressure under each leg (or caster) of your desk chair.
4. Estimate the number of times the ‘e’ key is pressed during the five year lifetime of your computer.
6. Estimate how long it takes to make an ice cube.
7. Estimate the bite pressure on your tooth surfaces when eating an apple.
8. Estimate the volume of a ton of bricks.
9. Estimate the track density of a 1 Gb hard disk.
Estimation Lecture -- Page 1