Post by tbw on May 8, 2013 11:12:06 GMT -5
Below are a series of graphs to help understand how critical it is in understanding how average's affect timeline's.
Benteen diverges from Custer's battalion. And at some point after departing Custer, Benteen stated that he observed the white horse troop at a
gallop. Just like any other time and motion study, it simply must be accurately ascertained where and when this sighting occurred. Can this be
done using averages?
There are two elements in this excercise that are cruicial, where - place, and when - time. And one can't be more or less important than the
other.
The convention used will be as the demonstration graph depicts below. X is point at which Custer and Benteen depart from each other. THe
degrees that separated them according to Benteen was 45° and the mid line across the graph depicts this degree. Each \ or / Represents 1/2 mile.
If a number appears on the graph it represents a portion of a mile, ie 5 = 1/5th mile, 6 = 1/6th mile, 8 = 1/8th mile etc. If a terrain feature
is placed on this graph its initial and an accompanying legend will report what that is. In the following example the Legend for M would be the
Morass and L would be LSH. At the top will appear a dotted line, completing the triangles, this line represents how far away they would be from
each other continuing awa from each other at a 45° angle. At the midline of the line is the distance stated in miles how far apart they would be
from each other.
For the following graphs, Benteen stated that he witnessed the white horse sighting event when he was about 45 minutes into his ride after
departure. And since it most testimony is contested concerning where they departed from each other, even where this sighting was made from. I
urge participation of all to present their thoughts on where and when they think these contested places were or might have been.
#1
Both commands walk at about 4 mph. In 45 minutes they would be about 3 miles from where they departed from each other .
#2
Both command fast walk/trot at about 5 mph. In 45 minutes they would be about 3 3/4ths miles from where they separated.
#3
Benteen said they went about 8 miles from where they departed Custer before turning back. The unknown here would be where Custer was when
Benteen did that. Benteen also stated that at that point he had been 1 & 1/2 hours in getting to that point. THis figures out at an average
speed of 5.3... mph Using this as a guide and using the same mph for Custer we get this when supposedly Benteen saw the white horses on the
gallop, they would have been 4 miles from where they departed, exactly the half way mark to where Benteen said they turned around.
#4
If Custer went at a faster speed than Benteen did, leaving Benteens miles and speed the same as #3, and then lets suppose Custer easily doubled
Benteen's speed (10.66 mph fast trot - maybe lope) because of that galloping white horse sighting, what would that look like. But this graph
doesn't show a "dead gallop" - "fast gallop" as benteen described it. For that, it might have been well in excess of 14 mph if Custer sustained
that speed.
#5
Then we have this:
Q. How far from the ford A did you receive your first orders from Gen.Custer?
A. Having gone to the left and come back again, it is hard to say; I suppose
it was about 15 miles in a direct line.
Q. How far towards the tepee do you suppose the column had advanced when
you lost sight of it?
A. The only company I saw was the gray horse company, and they were on a
fast gallop. They could have gone down there in an hour and three quarters
or two hours at the farthest.
Q. About how far from that tepee where you found the dead Warrior was
it, where Gen. Custer gave you the order to diverge with your battalion?
A, About eleven miles.
Q. In reference to the distance, how far do you suppose the command of General
Custer was from the tepee at the time you lost sight of the column?
A. I could not tell it might have been 5 or 6 miles or more.
He stated 15 miles for the circuit he made.
The distance from where he was sent to the tepee with the dead warrior he stated about 11 miles.
He was asked how far from that tepee was Custer at the time he lost sight of the column, he guessed 5-6 miles or more. because he couldn't see it
at that time.
When asked, how far towards the tepee Custer's was Custer when he lost sight of it. He guessed they could have gone down there in an hour and
3/4ths or 2 hours at the fartherst.
How far down Custer's trail, from the place where he had been sent, was it to where the tepee with the dead warrior in it was? He stated about
11 miles. He stated he made a 15 mile circuit, went about 8 out and about 7 back to the trail. Below is the graph for both.
#6
Since Benteen lost sight of Custer's battalion at about 45 minutes into his journey, he was asked How far towards the tepee do you suppose the
column had advanced when you lost sight of it? He answered, I could not tell it might have been 5 or 6 miles or more. He qualified that with
this statement. ...they could have gone down there in an hour and 3/4ths or 2 hours at the fartherst. This imposes a speed on Custer's column
of about 5.5 to 6 1/4th mph average. At 45 minutes into Benteen's ride, he spots the white horse troop on a gallop, admittedly a higher speed
than what Benteen averaged it when he witnessed them on a fast gallop. Below is the chart to that point when Benteen was 1/2 way in his journey
out, and where he observed them at. First chart (A) 5.5 mph, 2nd (B) 6.25 mph
#7
Now that we have Benteen's time estimates for both his own and Custer's pace, it can be figured where they were in relation to one another at any
given moment in time up to the place Benteen designated, "the tepee". These of course based upon his 'average' speed recollections of that time
given in testimony at the RCOI three years later.
So what do these mathematical charts show. They show by mathematical progression where each battalion was in relation to the other by mile and
hours (°), minutes (') and seconds ("). Benteen estimated several things in his testimony, granted they were guesses. How well did he do?
Q. How far from the ford A did you receive your first orders from Gen.Custer?
A. Having gone to the left and come back again, it is hard to say; I suppose
it was about 15 miles in a direct line.
Tested in the sense we used his 8 miles out at 45° angle and 7 miles back to the trail to understand the following.
Q. How far towards the tepee do you suppose the column had advanced when
you lost sight of it?
A. The only company I saw was the gray horse company, and they were on a
fast gallop. They could have gone down there in an hour and three quarters
or two hours at the farthest.
Chart A
The subject here was his estimate of time it would have taken, in time, for Custer to have gone the distance on to the tepee based upon Benteen's
sighting of the white horse troop at about the 1/2 way mark in Benten's ride (4 miles). His estimates. 1hour and 3/4ths up to 2 hours 'at the
farthest. Here is what the graphs show. The two paces 5.5 mph at 2 hours, and 6.25 mph at 1 hour 45 minutes show that at the 5.5 mph pace it
would have taken Custer 1°41'53" to have gone 10.6 miles (a mere .2 of a mile from the tepee), when Benteen at that time would have been 1 mile back (9 miles into journey) on his
return trip to the trail. At that time they would have been separated by about 10.1 miles. In the following Q&A Benteen reveals that it was
about 11 (the actual was 10.8 miles as figured by the mathematical progression, and will be the one used) miles to that tepee from where he
departed Custer. And in the 2nd Q&A, below the first, he said from that tepee back to where he sighted the white horse troop was about 5 to 6
miles. In the first estimate, chart A, 5.5 mph, 10.8 miles minus Custer's miles when Benteen sighted him (4.3) is 5.5 miles, right smack dab in
the middle of his estimate of 5 to 6 miles.
Because this is the slower pace of the two, and because Benteen stated that it might have taken him 1.75 up to 2 hours to have gone the distance
from where they departed. Chart A, by exact mathematical progression, and no finegling to have made it that way, shows that at that exact two
hour mark, Benteen would have been 3 miles back in his journey to the trail, 4 miles from it in fact. Custer would have been at the time of
Benteen's sighting 6.5 miles from that tepee at his 4 mile mark in his journey out, a mere half mile over his highest estimate of 6 miles. The
distance at that time separating the two columns. 8.3 miles.
Q. About how far from that tepee where you found the dead Warrior was
it, where Gen. Custer gave you the order to diverge with your battalion?
A, About eleven miles.
Q. In reference to the distance, how far do you suppose the command of General
Custer was from the tepee at the time you lost sight of the column?
A. I could not tell it might have been 5 or 6 miles or more.
Chart B
Again...the subject here was his estimate of time it would have taken, in time, for Custer to have gone the distance on to the tepee based upon
Benteen's sighting of the white horse troop at about the 1/2 way mark in Benten's ride (4 miles). His estimates. 1 hour and 3/4ths up to 2 hours
'at the farthest. Here is what this graphs show. The pace would have averaged out at 6.25 mph at 1 hour 45 minutes show that at the 6.25 mph
pace it would have taken Custer 1°41'53" to have gone 10.6 miles, when Benteen at that time would have been 1 mile back (9 miles into journey) on
his return trip to the trail. At that time they would have been separated by about 10.6 miles. In the following Q&A Benteen reveals that it was
about 11 (the actual was 10.8 miles as figured by the mathematical progression, and will be the one used) miles to that tepee from where he
departed Custer. And in the 2nd Q&A, below the first, he said from that tepee back to where he sighted the white horse troop was about 5 to 6
miles. In the 2nd estimate, chart B, @ 6.25 mph, 10.8 tepee miles minus Custer's miles when Benteen sighted him (4.75) is 6.02 miles, right at the higher of the two estimates (6) of his estimate of 5 to 6 miles.
The farthest apart the columns (Custer/Benteen) were was 11.5 miles (chart A) and 12.4 miles (chart B). At one time during the testimony at the Rcoi Benteen was asked how far from furthest point in their separation was Reno and his command from him. He estimated that distance as 15 miles. It would have been anywhere (reports conflict...so..) 3 to 4 miles on from the tepee Benteen mentions here. This mileage when added to the greatest separations mileage estimates (11.5 & 12.4) show this At 11.5 miles greatest separation between Custer and his own bttn. + 3 miles is 14.5 and 15.5 respectively at 4 miles. At 12.4 miles (chart B) greatest separation betwen Custer and his own bttn + 3 miles is 15.4 miles and respectively at 4 miles would be 16.4 miles.
Benteen diverges from Custer's battalion. And at some point after departing Custer, Benteen stated that he observed the white horse troop at a
gallop. Just like any other time and motion study, it simply must be accurately ascertained where and when this sighting occurred. Can this be
done using averages?
There are two elements in this excercise that are cruicial, where - place, and when - time. And one can't be more or less important than the
other.
The convention used will be as the demonstration graph depicts below. X is point at which Custer and Benteen depart from each other. THe
degrees that separated them according to Benteen was 45° and the mid line across the graph depicts this degree. Each \ or / Represents 1/2 mile.
If a number appears on the graph it represents a portion of a mile, ie 5 = 1/5th mile, 6 = 1/6th mile, 8 = 1/8th mile etc. If a terrain feature
is placed on this graph its initial and an accompanying legend will report what that is. In the following example the Legend for M would be the
Morass and L would be LSH. At the top will appear a dotted line, completing the triangles, this line represents how far away they would be from
each other continuing awa from each other at a 45° angle. At the midline of the line is the distance stated in miles how far apart they would be
from each other.
Benteen Custer
------------8.8-------------- Distance between columns
M L Codes for terrain features
4 5 partial miles
6 \ / 6 miles
\ /
\ /
\ /
\ /
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X diverging columns
For the following graphs, Benteen stated that he witnessed the white horse sighting event when he was about 45 minutes into his ride after
departure. And since it most testimony is contested concerning where they departed from each other, even where this sighting was made from. I
urge participation of all to present their thoughts on where and when they think these contested places were or might have been.
#1
Both commands walk at about 4 mph. In 45 minutes they would be about 3 miles from where they departed from each other .
Benteen Custer
----4.24-----
3 miles \ / 3 miles
\ --45°--/
\ /
\ /
\ /
\/
X
#2
Both command fast walk/trot at about 5 mph. In 45 minutes they would be about 3 3/4ths miles from where they separated.
Benteen Custer
------5.3------
.7 .7
3 miles \ / 3 miles
\ --45°--/
\ /
\ /
\ /
\/
X
.7 = 3/4th mile
#3
Benteen said they went about 8 miles from where they departed Custer before turning back. The unknown here would be where Custer was when
Benteen did that. Benteen also stated that at that point he had been 1 & 1/2 hours in getting to that point. THis figures out at an average
speed of 5.3... mph Using this as a guide and using the same mph for Custer we get this when supposedly Benteen saw the white horses on the
gallop, they would have been 4 miles from where they departed, exactly the half way mark to where Benteen said they turned around.
Benteen Custer
------5.6-------
4 \ / 4
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X
#4
If Custer went at a faster speed than Benteen did, leaving Benteens miles and speed the same as #3, and then lets suppose Custer easily doubled
Benteen's speed (10.66 mph fast trot - maybe lope) because of that galloping white horse sighting, what would that look like. But this graph
doesn't show a "dead gallop" - "fast gallop" as benteen described it. For that, it might have been well in excess of 14 mph if Custer sustained
that speed.
Benteen Custer
-----------8.94----------------
/ 8
/
/
/
/
/
/
/
4 \ /
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X
#5
Then we have this:
Q. How far from the ford A did you receive your first orders from Gen.Custer?
A. Having gone to the left and come back again, it is hard to say; I suppose
it was about 15 miles in a direct line.
Q. How far towards the tepee do you suppose the column had advanced when
you lost sight of it?
A. The only company I saw was the gray horse company, and they were on a
fast gallop. They could have gone down there in an hour and three quarters
or two hours at the farthest.
Q. About how far from that tepee where you found the dead Warrior was
it, where Gen. Custer gave you the order to diverge with your battalion?
A, About eleven miles.
Q. In reference to the distance, how far do you suppose the command of General
Custer was from the tepee at the time you lost sight of the column?
A. I could not tell it might have been 5 or 6 miles or more.
He stated 15 miles for the circuit he made.
The distance from where he was sent to the tepee with the dead warrior he stated about 11 miles.
He was asked how far from that tepee was Custer at the time he lost sight of the column, he guessed 5-6 miles or more. because he couldn't see it
at that time.
When asked, how far towards the tepee Custer's was Custer when he lost sight of it. He guessed they could have gone down there in an hour and
3/4ths or 2 hours at the fartherst.
How far down Custer's trail, from the place where he had been sent, was it to where the tepee with the dead warrior in it was? He stated about
11 miles. He stated he made a 15 mile circuit, went about 8 out and about 7 back to the trail. Below is the graph for both.
Benteen back Benteen out
-----------10.8----------------
/ 8
/
7 \ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X
#6
Since Benteen lost sight of Custer's battalion at about 45 minutes into his journey, he was asked How far towards the tepee do you suppose the
column had advanced when you lost sight of it? He answered, I could not tell it might have been 5 or 6 miles or more. He qualified that with
this statement. ...they could have gone down there in an hour and 3/4ths or 2 hours at the fartherst. This imposes a speed on Custer's column
of about 5.5 to 6 1/4th mph average. At 45 minutes into Benteen's ride, he spots the white horse troop on a gallop, admittedly a higher speed
than what Benteen averaged it when he witnessed them on a fast gallop. Below is the chart to that point when Benteen was 1/2 way in his journey
out, and where he observed them at. First chart (A) 5.5 mph, 2nd (B) 6.25 mph
A
Benteen Custer
-------5.7-------
8
4 \ / 4.125
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X
B
Benteen Custer
--------6.18-------
3
4 \ / 4.71
\ /
\ /
\ --45°--/
\ /
\ /
\ /
\/
X
8 on table A = 1/8th mile
3 on table B = 3/4ths mile
#7
Now that we have Benteen's time estimates for both his own and Custer's pace, it can be figured where they were in relation to one another at any
given moment in time up to the place Benteen designated, "the tepee". These of course based upon his 'average' speed recollections of that time
given in testimony at the RCOI three years later.
A
Benteen out8 Custer down tepee
---------------------45°-------------------
...................11.5....................
2°00'00" 3 mile /.........8.3.................../ 10.8 mile tepee
/ /
1°53'12" 2 mile /...........8.6................./ 10.4 mile
/ /
1°41'53" 1 mile /........... 10.1.............../ 9.3 mile
/ /
1°30'34" 8 mile \.............11.5............./ 8.3 mile
\ /
1°19'15" 7 mile \...........10.1.........../ 7.3 mile
\ /
1°07'55" 6 mile \.........8.6........../ 6.2 mile
\ /
56'36" 5 mile \.......7.2......../ 5.2 mile
\ /
45'17" 4 mile \.....5.9....../ 4.3 mile
\ /
33'58" 3 mile \...4.3..../ 3.1 mile
\ /
22'38" 2 mile \.2.9../ 2.1 mile
\ /
11'19" 1 mile \1.5/ 1 mile 135 ft.
\/
X
B
Benteen Out8 Custer down tepee
---------------------45°-------------------
---------------------12.4-------------------
3 mile / / 10.8 mile Tepee
/ /
2 mile / / 10.6 mile 1°41'53"
/ //
1°41'53" 1 mile /............10.6.....********/// 9.5 mile 1°30'34"
/ //
1°30'34" 8 mile \.............12.4....*******/// 8.3 mile 1°19'15"
\ //
1°19'15" 7 mile \...........10.9...******/// 7.1 mile 1°07'55"
\ //
1°07'55" 6 mile \..........9.3..*****/// 6 mile
\ /
56'36" 5 mile \........7.75....../ 5.9 mile
\ /
45'17" 4 mile \......6.2...../ 4 3/4 mile
\ /
33'58" 3 mile \....4.6.../ 3 1/2 mile
\ /
22'38" 2 mile \...3../ 2 1/3rd mile
\ /
11'19" 1 mile \1.5/ 1 1/6th mile
\/
X
So what do these mathematical charts show. They show by mathematical progression where each battalion was in relation to the other by mile and
hours (°), minutes (') and seconds ("). Benteen estimated several things in his testimony, granted they were guesses. How well did he do?
Q. How far from the ford A did you receive your first orders from Gen.Custer?
A. Having gone to the left and come back again, it is hard to say; I suppose
it was about 15 miles in a direct line.
Tested in the sense we used his 8 miles out at 45° angle and 7 miles back to the trail to understand the following.
Q. How far towards the tepee do you suppose the column had advanced when
you lost sight of it?
A. The only company I saw was the gray horse company, and they were on a
fast gallop. They could have gone down there in an hour and three quarters
or two hours at the farthest.
Chart A
The subject here was his estimate of time it would have taken, in time, for Custer to have gone the distance on to the tepee based upon Benteen's
sighting of the white horse troop at about the 1/2 way mark in Benten's ride (4 miles). His estimates. 1hour and 3/4ths up to 2 hours 'at the
farthest. Here is what the graphs show. The two paces 5.5 mph at 2 hours, and 6.25 mph at 1 hour 45 minutes show that at the 5.5 mph pace it
would have taken Custer 1°41'53" to have gone 10.6 miles (a mere .2 of a mile from the tepee), when Benteen at that time would have been 1 mile back (9 miles into journey) on his
return trip to the trail. At that time they would have been separated by about 10.1 miles. In the following Q&A Benteen reveals that it was
about 11 (the actual was 10.8 miles as figured by the mathematical progression, and will be the one used) miles to that tepee from where he
departed Custer. And in the 2nd Q&A, below the first, he said from that tepee back to where he sighted the white horse troop was about 5 to 6
miles. In the first estimate, chart A, 5.5 mph, 10.8 miles minus Custer's miles when Benteen sighted him (4.3) is 5.5 miles, right smack dab in
the middle of his estimate of 5 to 6 miles.
Because this is the slower pace of the two, and because Benteen stated that it might have taken him 1.75 up to 2 hours to have gone the distance
from where they departed. Chart A, by exact mathematical progression, and no finegling to have made it that way, shows that at that exact two
hour mark, Benteen would have been 3 miles back in his journey to the trail, 4 miles from it in fact. Custer would have been at the time of
Benteen's sighting 6.5 miles from that tepee at his 4 mile mark in his journey out, a mere half mile over his highest estimate of 6 miles. The
distance at that time separating the two columns. 8.3 miles.
Q. About how far from that tepee where you found the dead Warrior was
it, where Gen. Custer gave you the order to diverge with your battalion?
A, About eleven miles.
Q. In reference to the distance, how far do you suppose the command of General
Custer was from the tepee at the time you lost sight of the column?
A. I could not tell it might have been 5 or 6 miles or more.
Chart B
Again...the subject here was his estimate of time it would have taken, in time, for Custer to have gone the distance on to the tepee based upon
Benteen's sighting of the white horse troop at about the 1/2 way mark in Benten's ride (4 miles). His estimates. 1 hour and 3/4ths up to 2 hours
'at the farthest. Here is what this graphs show. The pace would have averaged out at 6.25 mph at 1 hour 45 minutes show that at the 6.25 mph
pace it would have taken Custer 1°41'53" to have gone 10.6 miles, when Benteen at that time would have been 1 mile back (9 miles into journey) on
his return trip to the trail. At that time they would have been separated by about 10.6 miles. In the following Q&A Benteen reveals that it was
about 11 (the actual was 10.8 miles as figured by the mathematical progression, and will be the one used) miles to that tepee from where he
departed Custer. And in the 2nd Q&A, below the first, he said from that tepee back to where he sighted the white horse troop was about 5 to 6
miles. In the 2nd estimate, chart B, @ 6.25 mph, 10.8 tepee miles minus Custer's miles when Benteen sighted him (4.75) is 6.02 miles, right at the higher of the two estimates (6) of his estimate of 5 to 6 miles.
The farthest apart the columns (Custer/Benteen) were was 11.5 miles (chart A) and 12.4 miles (chart B). At one time during the testimony at the Rcoi Benteen was asked how far from furthest point in their separation was Reno and his command from him. He estimated that distance as 15 miles. It would have been anywhere (reports conflict...so..) 3 to 4 miles on from the tepee Benteen mentions here. This mileage when added to the greatest separations mileage estimates (11.5 & 12.4) show this At 11.5 miles greatest separation between Custer and his own bttn. + 3 miles is 14.5 and 15.5 respectively at 4 miles. At 12.4 miles (chart B) greatest separation betwen Custer and his own bttn + 3 miles is 15.4 miles and respectively at 4 miles would be 16.4 miles.
