Track: Correlating Running Times versus Distance

Dear Long-Distance-Runner Nephew, William:  

Thinking about how to model expected running times (T, sec) versus distance (D, m),

I figured the relationship might be:

T sec = (10 sec) (D / 100 m)^b

Where b would be b=1.0 if you could run the entire distance at the same speed you ran the 100 m.

I expected fatigue would make b>1.0, but I did not know how much greater.

 

I consulted the internet:

 https://duckduckgo.com/?q=correlation+between+running+times+and+distances&t=chromentp&ia=web

 there the exponent was found to be b = 1.1 from 100m to 10 km.

The best world-record coefficient (e.g., 10 s) might be Bolt’s 9.6 s for the 100 m, but

I was most interested in the exponent, the dependence of time on distance.

 

In high school, I ran the mile in about 5 minutes = 300 sec.

My pitiful 100-yard dash time was about 12 sec.

The ratio of these times was about (300/12) = 25.0.

The ratio of the distances was mile/dash = (5280/300) = 17.6

Which predicts a time ratio of (17.6)^1.1 = 23.4

not too different from 25.0,  assuming my approximate 12 s estimate.

 For non-record-holders like myself, expect our times vs. our distances to go as 

(T/To) = (D/Do)^1.1. 

So, as you go from 6 k to 8 k, for example, you would expect a ratio of the times of about

(8/6)^1.1 = 1.37. 

A 6k time of 21 minutes would be about 21.0 x 1.37 = 28.8 minutes, rather than simply (8/6)(21.0)=28.0. The extra 0.8 of a minute is 48 seconds.

Doubling the distance would tend to increase the time by the multiplier (2)^1.1=2.14, which is 7% longer than 2.0.

 

To some degree, goals like these target times can be helpful.

At other times, they might be unrealistic, too easy, or too hard.

They are interesting, though. (I was sort of a theoretical miler.)

 

I view this as a way to judge the likely impact of distance on your time,

rather than a way to compare oneself against world record holders.

 

WRITING BETTER ENGLISH, WEEK 11

 

WRITING BETTER ENGLISH, WEEK 11

Persuasion:

ETHOS – AUTHORITY, REPUTATION, ACHIEVEMENT, INSIGHT

LOGOS - REASON

PATHOS – EMOTION

 

- STRUNK AND WHITE, from THE ELEMENTS OF STYLE

- EMERSON, from “SELF-RELIANCE”

-FROST, POETRY, ”The Oven Bird”

 

LAST WEEK’S ASSIGNMENT, 150-250 WORDS ON BROWNING’S “MY LAST DUCHESS’

 

 

 

NEXT WEEK’S ASSIGNMENT, 150-250 W0RDS

FROST’S ‘The Oven Bird” or on a quote from Emerson, 150-250 words

 

https://www.moralapologetics.com/wordpress/what-to-make-of-a-diminished-thing-poeticizing-the-fall-part-1-of-2

In his poem “The Oven Bird,” Frost uses the theological tropes of the Fall along with natural revelation to give new meaning to the natural world of the poem while also continuing to develop metaphorical poetics in which meaning itself must be both natural and supernatural. Frost displays remarkable poetic dexterity by both theologizing and naturalizing the act of this common bird’s call.

There is a singer everyone has heard,

Loud, a mid-summer and a mid-wood bird,

Who makes the solid tree trunks sound again.

He says that leaves are old and that for flowers

Mid-summer is to spring as one to ten.

He says the early petal-fall is past

When pear and cherry bloom went down in showers

On sunny days a moment overcast;

And comes that other fall we name the fall.

He says the highway dust is over all.

The bird would cease and be as other birds

But that he knows in singing not to sing.

The question that he frames in all but words

Is what to make of a diminished thing.

 

 

THE ELEMENTS OF STYLE, CONTINUED

IV. WORDS AND EXPRESSIONS COMMONLY MISUSED

“any body” means “any corpse. ”Use “anybody.”

“as good or better than.” Use “as good as, if not better.

“As yet.” Use “yet.”.”

“no” doubt but that” use “no doubt that

“Certainly” often over-used.

“Comprise” means embrace or include.

“Currently” is often reeundant.

“Data” is a plural noun. “Datum” is singular.

“disinterested” is impartial. “Uninterested” bored.

 

 

 

ESSAY, "SELF-RELIANCE," RALPH WALDO EMERSON

 

FIFTEENTH PARAGRAPH Ending

We pass for what we are.

Character teaches above our wills.

Men imagine that they communicate their virtue or vice only by overt actions, and do not see that virtue or vice emit a breath every moment.

SIXTEENTH PARAGRAPH (BROKEN INTO SENTENCES)

Fear never but you shall be consistent in whatever variety of actions, so they be each honest and natural in their hour.

For of one will, the actions will be harmonious, however unlike they seem.

These varieties are lost sight of when seen at a little distance, at a little height of thought. One tendency unites them all.

The voyage of the best ship is a zigzag line of a hundred tacks. This is only microscopic criticism. See the line from a sufficient distance, and it straightens itself to the average tendency.

Your genuine action will explain itself and will explain your other genuine actions. Your conformity explains nothing.

Act singly, and what you have already done singly will justify you now.

Greatness always appeals to the future. If I can be great enough now to do right and scorn eyes, I must have done so much right before as to defend me now.

Be it how it will, do right now. Always scorn appearances and you always may. The force of character is cumulative. All the foregone days of virtue work their health into this.

What makes the majesty of the heroes of the senate and the field, which so fills the imagination? The consciousness of a train of great days and victories behind.

There they all stand and shed an united light on the advancing actor. He is attended as by a visible escort of angels to every man’s eye.

That is it which throws thunder into Chatham’s voice, and dignity into Washington’s port, and America into Adams’s eye.

Honor is venerable to us because it is no ephemeris. It is always ancient virtue.

We worship it to-day because it is not of to-day. We love it and pay it homage because it is not a trap for our love and homage, but is self-dependent, selfderived, and therefore of an old immaculate pedigree, even if shown in a young person.

 

REMINDER  / REVIEW

Chapter Titles from THE 7 HABITS OF HIGHLY EFFECTIVE PEOPLE

Habit 1: Be Proactive
Habit 2: Begin with the End in Mind
Habit 3: Put First Things First
Habit 4: Think Win/Win
Habit 5: Seek First to Understand, Then to Be Understood
Habit 6: Synergize Habit

7: Sharpen the Saw

 

WRITING ASSIGNMENT:  150-250 WORDS ON AN EMERSON QUOTE OR ON FROST’S “THE OVEN BIRD”

 

 My other coaching site is WRITE YOUR BOOK WITH ME

 

WRITING BETTER ENGLISH, WEEK 10

Persuasion:

ETHOS – AUTHORITY, REPUTATION, ACHIEVEMENT, INSIGHT

LOGOS - REASON

PATHOS – EMOTION

 

- STRUNK AND WHITE, from THE ELEMENTS OF STYLE

- EMERSON, from “SELF-RELIANCE”

-BROWNING, POETRY, ”My Last Duchess”

 

LAST WEEK’S ASSIGNMENT, 150-250 WORDS ON FROST’S “A TIME TO TALK” OR ON A PARAGRAPH FROM EMERSON:

 

NEXT WEEK’S ASSIGNMENT, 150-250 W0RDS ON BROWNING’S “My Last Duchess”

 

My Last Duchess 

 

BY ROBERT BROWNING

 

FERRARA

 

That’s my last Duchess painted on the wall,

Looking as if she were alive. I call

That piece a wonder, now; Fra Pandolf’s hands

Worked busily a day, and there she stands.

Will’t please you sit and look at her? I said

“Fra Pandolf” by design, for never read

Strangers like you that pictured countenance,

The depth and passion of its earnest glance,

But to myself they turned (since none puts by

The curtain I have drawn for you, but I)

And seemed as they would ask me, if they durst,

How such a glance came there; so, not the first

Are you to turn and ask thus. Sir, ’twas not

Her husband’s presence only, called that spot

Of joy into the Duchess’ cheek; perhaps

Fra Pandolf chanced to say, “Her mantle laps

Over my lady’s wrist too much,” or “Paint

Must never hope to reproduce the faint

Half-flush that dies along her throat.” Such stuff

Was courtesy, she thought, and cause enough

For calling up that spot of joy. She had

A heart—how shall I say?— too soon made glad,

Too easily impressed; she liked whate’er

She looked on, and her looks went everywhere.

Sir, ’twas all one! My favour at her breast,

The dropping of the daylight in the West,

The bough of cherries some officious fool

Broke in the orchard for her, the white mule

She rode with round the terrace—all and each

Would draw from her alike the approving speech,

Or blush, at least. She thanked men—good! but thanked

Somehow—I know not how—as if she ranked

My gift of a nine-hundred-years-old name

With anybody’s gift. Who’d stoop to blame

This sort of trifling? Even had you skill

In speech—which I have not—to make your will

Quite clear to such an one, and say, “Just this

Or that in you disgusts me; here you miss,

Or there exceed the mark”—and if she let

Herself be lessoned so, nor plainly set

Her wits to yours, forsooth, and made excuse—

E’en then would be some stooping; and I choose

Never to stoop. Oh, sir, she smiled, no doubt,

Whene’er I passed her; but who passed without

Much the same smile? This grew; I gave commands;

Then all smiles stopped together. There she stands

As if alive. Will’t please you rise? We’ll meet

The company below, then. I repeat,

The Count your master’s known munificence

Is ample warrant that no just pretense

Of mine for dowry will be disallowed;

Though his fair daughter’s self, as I avowed

At starting, is my object. Nay, we’ll go

Together down, sir. Notice Neptune, though,

Taming a sea-horse, thought a rarity,

Which Claus of Innsbruck cast in bronze for me!

 

THE ELEMENTS OF STYLE, CONTINUED

IV. WORDS AND EXPRESSIONS COMMONLY MISUSED

“The truth is…,” “The fact is…, “Honestly…”  Just state it!

“They” Not with “each” “every” nor when it should be singular, “He” or “she.”

“This” often obscures what the reference is.

“Try and mend it” should be “Try to mend it.”
“Unique” does not have degrees of being unique.

“Utilize” is grandiose “use.”

 

 

ESSAY, "SELF-RELIANCE," RALPH WALDO EMERSON

FOURTEENTH PARAGRAPH

Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood.

 

FIFTEENTH PARAGRAPH

I suppose no man can violate his nature.

All the sallies of his will are rounded in by the law of his being, as the inequalities of Andes and Himmaleh are insignificant in the curve of the sphere.

Nor does it matter how you gauge and try him.

A character is like an acrostic or Alexandrian stanza;—read it forward, backward, or across, it still spells the same thing.

In this pleasing contrite wood-life which God allows me, let me record day by day my honest thought without prospect or retrospect, and I cannot doubt, it will be found symmetrical, though I mean it not and see it not.

My book should smell of pines and resound with the hum of insects.

The swallow over my window should interweave that thread or straw he carries in his bill into my web also.

We pass for what we are.

Character teaches above our wills.

Men imagine that they communicate their virtue or vice only by overt actions, and do not see that virtue or vice emit a breath every moment.

REMINDER  / REVIEW

Chapter Titles from THE 7 HABITS OF HIGHLY EFFECTIVE PEOPLE

Habit 1: Be Proactive
Habit 2: Begin with the End in Mind
Habit 3: Put First Things First
Habit 4: Think Win/Win
Habit 5: Seek First to Understand, Then to Be Understood
Habit 6: Synergize
Habit 7: Sharpen the Saw

WRITING ASSIGNMENT: 150-250 W0RDS ON BROWNING’S “My Last Duchess”

 

 

 

 

Queen or King – As sovereign, the King or Queen outranks everyone

Queen Consort – The Queen Consort is the wife of the King

Apart from the monarch and their spouse, the titles are:

·         Duke or Duchess

·         Marquess or Marchioness

·         Earl or Countess

·         Viscount or Viscountess

·         Baron or Baroness