xkcd: ?Physics Insight?
https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, they
put him in the history books. But when I do it, I get 'detained by >security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa. It is quite a ways
up. Articles can achieve significant velocity from there.
On Mon, 13 Oct 2025 17:22:10 -0500, Lynn McGuire
<lynnmcguire5@gmail.com> wrote:
xkcd: ?Physics Insight?
https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, they
put him in the history books. But when I do it, I get 'detained by >security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa. It is quite a ways >up. Articles can achieve significant velocity from there.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
In article <eqssekphm1g2ttdtq17kqqgo5krb90ub58@4ax.com>,
Paul S Person <psperson@old.netcom.invalid> wrote:
On Mon, 13 Oct 2025 17:22:10 -0500, Lynn McGuire
<lynnmcguire5@gmail.com> wrote:
xkcd: ?Physics Insight?
https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, they
put him in the history books. But when I do it, I get 'detained by
security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa. It is quite a ways >>> up. Articles can achieve significant velocity from there.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
I have some doubts on whether that concept would occur to him. IIRC, the whole idea of "Time on Target" was for explosive shells.
On 10/14/2025 12:09 PM, Robert Woodward wrote:
In article <eqssekphm1g2ttdtq17kqqgo5krb90ub58@4ax.com>,
˙ Paul S Person <psperson@old.netcom.invalid> wrote:
On Mon, 13 Oct 2025 17:22:10 -0500, Lynn McGuire
<lynnmcguire5@gmail.com> wrote:
xkcd: ?Physics Insight?
˙˙˙ https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, they >>>> put him in the history books.˙ But when I do it, I get 'detained by
security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa.˙ It is quite a
ways
up.˙ Articles can achieve significant velocity from there.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
I have some doubts on whether that concept would occur to him. IIRC, the
whole idea of "Time on Target" was for explosive shells.
Were explosive shells used before the USA Civil War ?
On 10/14/2025 4:26 PM, Lynn McGuire wrote:
On 10/14/2025 12:09 PM, Robert Woodward wrote:
In article <eqssekphm1g2ttdtq17kqqgo5krb90ub58@4ax.com>,
˙ Paul S Person <psperson@old.netcom.invalid> wrote:
On Mon, 13 Oct 2025 17:22:10 -0500, Lynn McGuire
<lynnmcguire5@gmail.com> wrote:
xkcd: ?Physics Insight?
˙˙˙ https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, they >>>>> put him in the history books.˙ But when I do it, I get 'detained by
security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa.˙ It is quite a >>>>> ways
up.˙ Articles can achieve significant velocity from there.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
I have some doubts on whether that concept would occur to him. IIRC, the >>> whole idea of "Time on Target" was for explosive shells.
Were explosive shells used before the USA Civil War ?
Do you know the words to "The Star-Spangled Banner?"
(Earlier possibilities include 13th century China and 14th century Venice.)
On 10/14/2025 3:57 PM, Mark Jackson wrote:
On 10/14/2025 4:26 PM, Lynn McGuire wrote:
On 10/14/2025 12:09 PM, Robert Woodward wrote:
In article <eqssekphm1g2ttdtq17kqqgo5krb90ub58@4ax.com>,
˙ Paul S Person <psperson@old.netcom.invalid> wrote:
On Mon, 13 Oct 2025 17:22:10 -0500, Lynn McGuire
<lynnmcguire5@gmail.com> wrote:
xkcd: ?Physics Insight?
˙˙˙ https://xkcd.com/3154/
?When Galileo dropped two weights from the Leaning Tower of Pisa, >>>>>> they
put him in the history books.˙ But when I do it, I get 'detained by >>>>>> security' for ?injuring several tourists.??
I have been to the top of the Leaning Tower of Pisa.˙ It is quite >>>>>> a ways
up.˙ Articles can achieve significant velocity from there.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
I have some doubts on whether that concept would occur to him. IIRC,
the
whole idea of "Time on Target" was for explosive shells.
Were explosive shells used before the USA Civil War ?
Do you know the words to "The Star-Spangled Banner?"
(Earlier possibilities include 13th century China and 14th century
Venice.)
Ah !˙ Very true.
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how things
fell.
I know of Venetian use in the 15th century.
Paul S Person <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target" >>computations [1] never worked with Aristotle's view of how things
fell.
_Two New Sciences_ has a discussion of this and is well worth
reading. Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of Newton's.
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan artillery.
I wonder if he was trying to find out why their "time on target" >>>computations [1] never worked with Aristotle's view of how things
fell.
_Two New Sciences_ has a discussion of this and is well worth
reading. Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of Newton's.
I take that back. I thought there was a discussion of time of flight
but looking it up I find there is not.... it would be difficult to do >without the calculus I suspect.
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading. Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back. I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
On 10/15/2025 10:34 AM, Scott Dorsey wrote:
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to which
a given distance/angle table applies?˙ Then, assuming no meaningful
impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
I appear to be projecting much more modern concepts of artillery onto
the distant past.
Ancient geometry did include conic sections, although whether they
were related to the path of missiles used in indirect fire [1] I do
not know.=20
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars applied mathematics to gunnery, possibly Dr Dee before he became an occultist.
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
The Parliamentary officer Nathaniel Nye directed cannon in the English
civil war and published a book on the mathematics of it in 1647, in
which he cited a much earlier Italian mathematician, Tartaliga, who
wrote on the subject in 1537.
William Hyde
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars applied
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person? <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.? Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.? I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.? Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?? Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
mathematics to gunnery, possibly Dr Dee before he became an occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the English
civil war and published a book on the mathematics of it in 1647, in
which he cited a much earlier Italian mathematician, Tartaliga, who
wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Paul S Person <psperson@old.netcom.invalid> wrote:
I appear to be projecting much more modern concepts of artillery onto
the distant past.
Ancient geometry did include conic sections, although whether they
were related to the path of missiles used in indirect fire [1] I do
not know.=20
I don't know, but Galileo does talk about how the projectile follows a parabola and why. He does mention indrect fire although I don't think
it is very useful unless you have good spotting, which would have been
a problem at the time.
On Wed, 15 Oct 2025 22:00:02 -0400, Cryptoengineer
<petertrei@gmail.com> wrote:
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars applied
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target" >>>>>>> computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
mathematics to gunnery, possibly Dr Dee before he became an occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the English
civil war and published a book on the mathematics of it in 1647, in
which he cited a much earlier Italian mathematician, Tartaliga, who
wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
While researching the history of "time on target", I found a Wikipedia article asserting that it was developed by the Brits in North Africa
in 1941 or 1942.
Fixed charges I don't know about, but computers (if you mean modern
digital computers) they did not have.
OTOH, a book I purchased, /The Effects of Nuclear Weapons/, has a sort
of circular slide rule that /could/ be considered a computer of such
effects. So some such "computer" might have been involved.
And then developed further by the Americans as the war progressed.
Please remember that Aubrey makes sh*t up.
So do lots of people. We live in an age when "skepticism" is not
restricted to the paranormal, or religion, but extends to everything.
Scott Dorsey <kludge@panix.com> schrieb:
Paul S Person <psperson@old.netcom.invalid> wrote:
I appear to be projecting much more modern concepts of artillery onto
the distant past.
Ancient geometry did include conic sections, although whether they
were related to the path of missiles used in indirect fire [1] I do
not know.=20
I don't know, but Galileo does talk about how the projectile follows a
parabola and why. He does mention indrect fire although I don't think
it is very useful unless you have good spotting, which would have been
a problem at the time.
If you are firing over a wall into a fortress or a city, it is
not that much of a problem.
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars applied
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target"
computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
mathematics to gunnery, possibly Dr Dee before he became an occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the English
civil war and published a book on the mathematics of it in 1647, in
which he cited a much earlier Italian mathematician, Tartaliga, who
wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Paul S Person <psperson@old.netcom.invalid> wrote:
I appear to be projecting much more modern concepts of artillery onto
the distant past.
Ancient geometry did include conic sections, although whether they
were related to the path of missiles used in indirect fire [1] I do
not know.=20
I don't know, but Galileo does talk about how the projectile follows a parabola and why. He does mention indrect fire although I don't think
it is very useful unless you have good spotting, which would have been
a problem at the time.
But time of arrival is more difficult since the projectile velocity
isn't constant at every point along that parabola. Vectors and the
calculus make these simple problems but they would be difficult to
solve without them.
On 10/15/2025 5:04 PM, Scott Dorsey wrote:
But time of arrival is more difficult since the projectile velocity
isn't constant at every point along that parabola. Vectors and the
calculus make these simple problems but they would be difficult to
solve without them.
Again, why would you need calculus? The time to arrival depends on the >distance to target and the horizontal component of the muzzle velocity,
both of which are constant. Only the vertical component of the shell's >velocity varies, and that doesn't enter into things.
(For negligible air resistance, of course, and - to be precise - firing
at a target at the same height as the cannon. Firing uphill the shell
will land a bit earlier, downhill a bit later.)
--
Mark Jackson - https://mark-jackson.online/
Against the assault of laughter nothing can stand.
- Mark Twain
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Cryptoengineer wrote:
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars applied
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target" >>>>>>> computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
mathematics to gunnery, possibly Dr Dee before he became an occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the
English civil war and published a book on the mathematics of it in
1647, in which he cited a much earlier Italian mathematician,
Tartaliga, who wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Well, he didn't have much of a BS detector, and never met a good story
he didn't spread, but I wasn't aware that he consciously lied.
On 10/15/2025 9:00 PM, Cryptoengineer wrote:
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Infantry light mortar platoon (81mm) leader, 1979. The light platoons
and the heavy mortar platoon (4.2 in) would practice ToT coordination
and we didn't use liquid propellant or computers. We used manual
plotting boards. The big boys would do the same with 105mm, 155mm, 8
inch and even naval big guns if available. It was rarely done on the fly
as it took time to set up and coordinate. Nowadays it is done by
computer and could be done on the fly. Target coordinates are entered,
the fire control computer figures bearing, elevation, charge for each
tube and transmits the data to each section. Guns are laid and somebody yells fire at the correct time.
Mark Jackson <mjackson@alumni.caltech.edu> wrote:
On 10/15/2025 5:04 PM, Scott Dorsey wrote:
But time of arrival is more difficult since the projectile velocity
isn't constant at every point along that parabola. Vectors and the
calculus make these simple problems but they would be difficult to
solve without them.
Again, why would you need calculus? The time to arrival depends on the
distance to target and the horizontal component of the muzzle velocity,
both of which are constant. Only the vertical component of the shell's
velocity varies, and that doesn't enter into things.
(For negligible air resistance, of course, and - to be precise - firing
at a target at the same height as the cannon. Firing uphill the shell >>will land a bit earlier, downhill a bit later.)
That's the point of indirect fire! You're firing upward and the shell >travels often higher vertically than it travels horizontally. The enemy
may not be very far away but they are on the other side of a barrier.
You can shoot over the barrier with artillery, while you are protected
from small arms fire. Angles of 75 to 85 degrees are not uncommon.
In article <l4p4fkt4705hetqgbd1k80ieb3ri6vl1d5@4ax.com>,
Paul S Person <psperson@old.netcom.invalid> wrote:
On Thu, 16 Oct 2025 20:18:07 -0400 (EDT), kludge@panix.com (Scott
Dorsey) wrote:
Mark Jackson <mjackson@alumni.caltech.edu> wrote:
On 10/15/2025 5:04 PM, Scott Dorsey wrote:
But time of arrival is more difficult since the projectile velocity
isn't constant at every point along that parabola. Vectors and the
calculus make these simple problems but they would be difficult to
solve without them.
Again, why would you need calculus? The time to arrival depends on the >>>> distance to target and the horizontal component of the muzzle velocity, >>>> both of which are constant. Only the vertical component of the shell's >>>> velocity varies, and that doesn't enter into things.
(For negligible air resistance, of course, and - to be precise - firing >>>> at a target at the same height as the cannon. Firing uphill the shell >>>> will land a bit earlier, downhill a bit later.)
That's the point of indirect fire! You're firing upward and the shell
travels often higher vertically than it travels horizontally. The enemy >>> may not be very far away but they are on the other side of a barrier.
You can shoot over the barrier with artillery, while you are protected
from small arms fire. Angles of 75 to 85 degrees are not uncommon.
Modern indirect fire, which does indeed require some form of spotting.
But the ancients shot arrows up and over the enemy, not because they
could not see them, but because they wanted to wound/kill /all/ of
them, not just those in the front line. The ones behind the front line
were, not hidden, but covered.
The Roman testudo <https://en.wikipedia.org/wiki/Testudo_formation>
was used to protect the troops against indirect arrow fire. (And also
to protect them from items falling off the walls of besieged cities --
things like stones, burning oil, and other nasties).
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
In article <10cu15t$19nk5$1@dont-email.me>,
Cryptoengineer <petertrei@gmail.com> wrote:
On 10/17/2025 12:09 PM, Ted Nolan <tednolan> wrote:
In article <l4p4fkt4705hetqgbd1k80ieb3ri6vl1d5@4ax.com>,
Paul S Person <psperson@old.netcom.invalid> wrote:
On Thu, 16 Oct 2025 20:18:07 -0400 (EDT), kludge@panix.com (Scott
Dorsey) wrote:
Mark Jackson <mjackson@alumni.caltech.edu> wrote:
On 10/15/2025 5:04 PM, Scott Dorsey wrote:
But time of arrival is more difficult since the projectile velocity >>>>>>> isn't constant at every point along that parabola. Vectors and the >>>>>>> calculus make these simple problems but they would be difficult to >>>>>>> solve without them.
Again, why would you need calculus? The time to arrival depends on the >>>>>> distance to target and the horizontal component of the muzzle velocity, >>>>>> both of which are constant. Only the vertical component of the shell's >>>>>> velocity varies, and that doesn't enter into things.
(For negligible air resistance, of course, and - to be precise - firing >>>>>> at a target at the same height as the cannon. Firing uphill the shell >>>>>> will land a bit earlier, downhill a bit later.)
That's the point of indirect fire! You're firing upward and the shell >>>>> travels often higher vertically than it travels horizontally. The enemy >>>>> may not be very far away but they are on the other side of a barrier. >>>>> You can shoot over the barrier with artillery, while you are protected >>>> >from small arms fire. Angles of 75 to 85 degrees are not uncommon.
Modern indirect fire, which does indeed require some form of spotting. >>>>
But the ancients shot arrows up and over the enemy, not because they
could not see them, but because they wanted to wound/kill /all/ of
them, not just those in the front line. The ones behind the front line >>>> were, not hidden, but covered.
The Roman testudo <https://en.wikipedia.org/wiki/Testudo_formation>
was used to protect the troops against indirect arrow fire. (And also
to protect them from items falling off the walls of besieged cities -- >>>> things like stones, burning oil, and other nasties).
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
I've heard the first two lines many times.
Is it a quote from a longer poem?
pt
Yes:
The Arrow and the Song
By Henry Wadsworth Longfellow
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
I breathed a song into the air,
It fell to earth, I knew not where;
For who has sight so keen and strong,
That it can follow the flight of song?
Long, long afterward, in an oak
I found the arrow, still unbroke;
And the song, from beginning to end,
I found again in the heart of a friend.
Bullwinkle the Moose also did a memorable version of it.
https://www.youtube.com/watch?v=Sfj744oqB0g
On 10/16/2025 4:03 PM, William Hyde wrote:
Cryptoengineer wrote:
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on target" >>>>>>>> computations [1] never worked with Aristotle's view of how
things fell.
_Two New Sciences_ has a discussion of this and is well worth
reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to
which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle).
applied mathematics to gunnery, possibly Dr Dee before he became an
occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the
English civil war and published a book on the mathematics of it in
1647, in which he cited a much earlier Italian mathematician,
Tartaliga, who wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Well, he didn't have much of a BS detector, and never met a good story
he didn't spread, but I wasn't aware that he consciously lied.
I seen articles where his colorful 'British naval jargon' is shown to
lack any contemporary examples.
Cryptoengineer wrote:
On 10/16/2025 4:03 PM, William Hyde wrote:
Cryptoengineer wrote:
On 10/15/2025 4:30 PM, William Hyde wrote:
Mark Jackson wrote:
On 10/15/2025 10:34 AM, Scott Dorsey wrote:I seem to recall from Aubrey that one of Elizabeth's scholars
Scott Dorsey <kludge@panix.com> wrote:
Paul S Person˙ <psperson@old.netcom.invalid> wrote:
IIRC, at some point Galileo was in charge of the Pisan
artillery.
I wonder if he was trying to find out why their "time on
target" computations [1] never worked with Aristotle's view of how >>>>>>>>> things fell.
_Two New Sciences_ has a discussion of this and is well worth >>>>>>>> reading.˙ Note that Galileo is thinking throughout of bodies
attracted to the earth and never makes that great jump of
Newton's.
I take that back.˙ I thought there was a discussion of time of
flight but looking it up I find there is not.... it would be
difficult to do without the calculus I suspect.
Probably not.˙ Did they know the muzzle velocity of the devices to >>>>>> which a given distance/angle table applies?˙ Then, assuming no
meaningful impact of air resistance:
time-to-target = distance divided by (muzzle velocity)*cos(angle). >>>>>>
applied mathematics to gunnery, possibly Dr Dee before he became an >>>>> occultist.
The Parliamentary officer Nathaniel Nye directed cannon in the
English civil war and published a book on the mathematics of it in
1647, in which he cited a much earlier Italian mathematician,
Tartaliga, who wrote on the subject in 1537.
William Hyde
"Time on target" involves firing several projectiles, setting the
propellent charges, firing times, and elevation of the cannon(s)
to cause the shells to arrive at the target simultaneously.
I've seen this done using cannon that have liquid propellants
and computer control. I can't imagine it being done with fixed
charges, or without computers, save as the result of a careful
iterative set of firings to zero on on the charges, timing and
elevations needed.
Please remember that Aubrey makes sh*t up.
Well, he didn't have much of a BS detector, and never met a good
story he didn't spread, but I wasn't aware that he consciously lied.
I seen articles where his colorful 'British naval jargon' is shown to
lack any contemporary examples.
Ah, we're talking about different Aubreys.
I should have been clearer.˙ I found this reference in John Aubrey's
"Brief Lives". Sorry about that.
And any such person would have been at least a generation after Tartaliga.
Infantry light mortar platoon (81mm) leader, 1979. The light platoons
and the heavy mortar platoon (4.2 in) would practice ToT coordination
and we didn't use liquid propellant or computers. We used manual
plotting boards. The big boys would do the same with 105mm, 155mm, 8
inch and even naval big guns if available. It was rarely done on the fly
as it took time to set up and coordinate. Nowadays it is done by
computer and could be done on the fly. Target coordinates are entered,
the fire control computer figures bearing, elevation, charge for each
tube and transmits the data to each section. Guns are laid and somebody yells fire at the correct time.
In article <10cu15t$19nk5$1@dont-email.me>,
Cryptoengineer <petertrei@gmail.com> wrote:
On 10/17/2025 12:09 PM, Ted Nolan <tednolan> wrote:
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
I've heard the first two lines many times.
Is it a quote from a longer poem?
pt
Yes:
The Arrow and the Song
By Henry Wadsworth Longfellow
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
I breathed a song into the air,
It fell to earth, I knew not where;
For who has sight so keen and strong,
That it can follow the flight of song?
Long, long afterward, in an oak
I found the arrow, still unbroke;
And the song, from beginning to end,
I found again in the heart of a friend.
Bullwinkle the Moose also did a memorable version of it.
https://www.youtube.com/watch?v=Sfj744oqB0g
Thanks for catching that. I'm surprised and impressed that 'time on
target' can be achieved without computers, but the idea of getting
with muzzle-loading black powder cannon on a ship at sea was ludicrous.
Jay Morris <morrisj@epsilon3.me> schrieb:
Infantry light mortar platoon (81mm) leader, 1979. The light platoons
and the heavy mortar platoon (4.2 in) would practice ToT coordination
and we didn't use liquid propellant or computers. We used manual
plotting boards. The big boys would do the same with 105mm, 155mm, 8
inch and even naval big guns if available. It was rarely done on the fly
as it took time to set up and coordinate. Nowadays it is done by
computer and could be done on the fly. Target coordinates are entered,
the fire control computer figures bearing, elevation, charge for each
tube and transmits the data to each section. Guns are laid and somebody
yells fire at the correct time.
The Panzerhaubitze 2000 can land up to 5 155 mm shells at the same
time on the same spot.
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