HP 20S and HP 21S: Approximating Stopping Distances

HP 20S and HP 21S:  Approximating Stopping Distances 

Introduction

We can approximate the stopping distance (in feet) of a vehicle on dry pavement given the vehicle's speed (in miles per hour, mph) by the formula: 

y = 3.85714285714*10^-2 * x^2 + 1.44504201681 * x + 0.64915966369

or

y = 27/200 * x^2 + 1.44504201681 * x + 0.64915966369

y:  stopping distance on dry pavement, feet
x:  speed of vehicle, mph

Assumptions:

*  The vehicle is assumed to be a passenger vehicle.

*  The reaction time is 1 second and the deceleration rate is 28 ft/s.

The program listed rounds all results to one decimal place.

HP 20S and HP 21S Program: Stopping Distance

The key codes for both calculators are the same in this program.

STEP KEY    KEY CODE
01   LBL B  61, 41, b
02   STO 0  21, 0
03   x^2    51, 11
04   ×      55
05   2      2
06   7      7
07   ÷      45
08   7      7
09   0      0
10   0      0
11   +      75
12   RCL 0  22, 0
13   ×      55
14   1      1
15   .      73
16   4      4
17   4      4
18   5      5
19   0      0
20   4      4
21   2      2
22   0      0
23   1      1
24   6      6
25   8      8
26   1      1
27   +      75
28   .      73
29   6      6
30   4      4
31   9      9
32   1      1
33   5      5
34   9      9
35   6      6
36   6      6
37   3      3
38   9      9
39   =      74
40   STO 1  21, 1
41   FIX 1  51, 33, 1
42   RTN    61, 26

Examples

Input:  25 mph,  Result:  60.9 ft

Input:  40 mph,  Result:  120.2 ft

Input:  65 mph,  Result:  257.5 ft

Note:  This time I am writing this blog entry direct in the Blogger compose box.  When I transfer text from either Jarte or WordPad to Blogger, all the formatting is lost.  And I don't want to format my text twice.  I will still save a backup copy.  I am very happy that Blogger compose box allows me to select special characters for the math symbols I need (the happy face is appropriate because it makes me happy!) 

Source:  

Glover, Thomas J.  Pocket Ref 4th Edition.  Sequoia Publishing, Inc. Littleton, CO. 2012

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Estimating the Boiling Point at Various Elevations

Estimating the Boiling Point at Various Elevations

Equation

We can estimate the boiling point of water, accurate to the nearest tenth (one decimal point), by the formula:

y = 4.299969165*10^-8 * x^2 – 0.0035531324 * x + 100.0049216

Where:

x = elevation in meters

y = boiling point of water in degrees Celsius (°C)

This equation was derived using quadratic regression analysis of 27 sample points, testing points for elevations from -305 m to 6629 m.

If you are working with US units, you can use the following unit conversions:

1 ft = 0.3048 m

Conversion to Celsius:  °C = (°F – 32) * 5/9

Examples

x = -152 m (approx. -498.687664 ft), y ≈ 100.5 °C

x = 4115 m (13500.65617 ft), y ≈ 86.1 °C

x = 6325 m (20751.31234 ft), y ≈ 79.3°

Source:

Glover, Thomas J.  Pocket Ref 4th Edition.  Sequoia Publishing, Inc. Littleton, CO. 2012

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Spring has Sprung: Pocket Ref, TI-30XA, Old HP Manuals, Review and more HP 39gii is coming

Hi everyone! Greetings from the Starbucks in Azusa, CA. Today's blog entry is a hodgepodge. Part 5 of the HP 39gii Programming tutorial - I am planning to have that ready by next week; totally apologize for the long delay.

I am very thankful my family is doing fine and my dad and uncle are both home from the hospital.

Pocket Ref: A Book of Everything?

While at Harbor Freight I found this book: "Pocket Ref 4th Edition" compiled by Thomas J. Glover; picked it up for $10. This reference edition has practically everything technical: physics, computer, mechanics, construction, automotive equations, electrical engineering equations, table of elements and chemical molecules, weights, densities, and perpetual calendars; just to name a few topics. This book has become a permanent part of things I take everywhere. Hopefully this reference will be used for future blog entries.

The TI-30XA: Then and Now

I finally broke down and got a new version of the TI-30XA by Texas Instruments. I have been resisting it for so long since I preferred the solar version over the battery version. What got me to finally purchase it is the article I saw on www.datamath.org, which details the logarithm bug.

Basically, the calculation goes haywire for:

(1) ln(1+x) when x is really small, and

(2) (1+1/n)^n for really large n.

I tested both calculations for the calculators. I also used the built in calculator in the google.com search engine. If you type in a mathematical calculation in google, it will get you the answer! Google also handles conversions and graphing functions.

Both the TI-30XAs (solar and battery) returned the same answers, so nothing has changed in the algorithm.

(1) ln(1 + x)

x=10^-2
TI-30XA: 0.009950331
Google: 0.00995033085

x=10^-8
TI-30XA: 0.000000001
Google: about 9.9 x 10^-9

(2) (1+1/n)^n

n = 10^2
TI-30XA: 2.70481383
Google: 2.70481382942

n = 10^8
TI-30XA: 2.7183727
Google: 2.7182817935


Out of curiosity, the TI-84+ agrees with Google. So this is a cautionary tale with the TI-30XA: be careful with arguments involving 1+x, where x is real small (like powers of 10^-6 or smaller) in any calculations involving logarithms and powers.

On the plus side, the battery TI-30XA retains memory when the ON button is pressed and the numbers are larger and in bold.

Review of the TI-84+ Color Silver Edition Coming Soon

Speaking of Texas Instruments calculators, my TI-84+ C Silver Edition is going to arrive at my doorstep in the coming week. That was my birthday present to myself. By clicking in this sentence, you can read how I initially felt about the TI-84+ CSE. I did read good reviews about it (This sentence is a link to one review, done by Christopher Mitchell (Cemetech). )and will give an impression when I actually have a TI-84+ CSE in my hands.

Old Hewlett Packard Manuals: They have a calculation manual for everything!

Back in the 1970s and 1980s, when pocket calculators were in their beginning stages, Hewlett Packard released detailed calculator manuals for not only their products (HP 35, HP 45, HP 67, etc), they had manuals covering almost every topic conceivable. To name a few: engineering, finance, games, biology, and one even covered astrology. Every now and then I like to study some of these manuals and try to see if I can do it (mostly with today's calculators). It is a really fun way to pass the time.

Several years ago, I ordered the DVD that contains a collection of manuals from The Museum of HP Calculators. You can order the DVD by clicking on this link.. The link will contain another link of the manuals the DVDs contain. I hope to refer to these manuals in future blog entries.

So, more HP 39gii Programming Tutorial, a review of the TI-84+ CSE, and more is coming. Thank you as always and take care,

Eddie


This blog is property of Edward Shore. 2013