Using Sound of Target Impact for Acoustic Reconstructions of Shooting Events
At page 2:
A microphone was placed a few centimeters from the muzzle to record both the muzzle blast and the sound of the bullet hitting the deer. The time recorded between the muzzle blast and bullet striking the target represents the sum of the bullet time of flight (tb) and the time for the sound to return to the microphone from the target (ts),
t = ts + tb = d/Vs + d/Vb
where d is the target distance, Vs is the velocity of sound, and Vb is the average bullet velocity over the distance.
At page 5:
These results show that it is possible to use an audio recording of a shooting event to accurately determine the distance between the target and the shooter. In cases where the location of the microphone is different, the mathematical details are different, but the ideas are the same.
At page 6:
A significant weakness in the study is the placement of the microphone near the muzzle of the gun, an unlikely location in most forensic cases....
Your recording is at a taxi nearly 400 feet away from the muzzle. You can do all the calculations you desire and the microphone will be no closer to the muzzle. The muzzle was likely around the corner, about 340 feet up, and some angular distance away from the microphone in the taxi. There was no direct path for the sound to reach the taxi.
The taxi did not pick up the sounds of the bullets striking people on the ground over 1200 feet away. The muzzle blast echoed back, but you do not know where from, or what path it took to the taxi at ground level.
A taxi recording indicates the muzzle blast with a delay by the time the sound took to reach the taxi, about .35 seconds at 400 feet. During that delay, the muzzle blast is on its way to some reflective surface which redirects the sound by some route to the taxi at ground level.
The elapsed time at the 400 foot distant taxi is not the elapsed time of the muzzle burst soundwave out and back. You ignored the ~0.35 second initial delay to reach the taxi, and you have no idea what reflective surface(s) redirected the sound before the echo arrived at the taxi.
You do have a nice picture with circles on it though.
The problem, of course, is related in your reference study.
Nope. I only referenced that study for the 2nd analysis - of audio/video recorded on the field. That analysis was done to refute the claim that a 2nd shooter, dressed as a policeman, was firing on the field. The observable difference between the bullet and report sound events succinctly refutes the asserted "proof" of a 2nd shooter on the field.
Regarding my initial meme "TEST FOR ECHO" -- Balistic data is NOT required to determine the total distance sound traveling from, and echoing back to, the ORIGIN point which is essentially where the Taxi driver was.
What would the Elapsed time between the Last Report sound event and the Last Bullet sound event be if, as the video alleged, the guy "dressed as police" was shooting?
Regarding my initial meme "TEST FOR ECHO" -- Balistic data is NOT required to determine the total distance sound traveling from, and echoing back to, the ORIGIN point which is essentially where the Taxi driver was.
The taxi was hardly at or near the origin point. It was 338+ feet away. The study placed a microphone "a few centimers" from the muzzle, not 10,302+ centimeters away.
The taxi was 338 feet down, some distance out from the building. Even if directly opposite the taxi, the muzzle had to travel 338+ feet to get to the taxi. That still take 0.299 seconds for the muzzle blast to reach the taxi from 338 feet.
Adjusting for your cited claim (at #118) that NYT reporting "suggests that Paddock was positioned directly above the camera at this point," with the taxi directly below the window, your blather has not materially changed the problem with your chartoon. The taxi microphone was not a few centimeters from the muzzle, it was over 338 feet away.
Yeah, you make believe that the sounds recorded in the taxi can yield an accurate measurement of distance.
The problem, of course, is related in your reference study.
Using Sound of Target Impact for Acoustic Reconstructions of Shooting Events
At page 2:
A microphone was placed a few centimeters from the muzzle to record both the muzzle blast and the sound of the bullet hitting the deer. The time recorded between the muzzle blast and bullet striking the target represents the sum of the bullet time of flight (tb) and the time for the sound to return to the microphone from the target (ts),
t = ts + tb = d/Vs + d/Vb
where d is the target distance, Vs is the velocity of sound, and Vb is the average bullet velocity over the distance.
At page 5:
These results show that it is possible to use an audio recording of a shooting event to accurately determine the distance between the target and the shooter. In cases where the location of the microphone is different, the mathematical details are different, but the ideas are the same.
At page 6:
A significant weakness in the study is the placement of the microphone near the muzzle of the gun, an unlikely location in most forensic cases....
Your recording is at a taxi over 338 feet away from the muzzle. You can do all the calculations you desire and the microphone will be no closer to the muzzle. The muzzle was likely around the corner, about 338 feet up, and some angular distance away from the microphone in the taxi.
The taxi did not pick up the sounds of the bullets striking people on the ground over 1200 feet away. The muzzle blast echoed back, but you do not know where from, or what path it took to the taxi at ground level.
A taxi recording indicates the muzzle blast with a delay by the time the sound took to reach the taxi, about .299 seconds at 338 feet. During that delay, the muzzle blast is on its way to some reflective surface which redirects the sound by some route to the taxi at ground level.
The elapsed time at the 338+ foot distant taxi is not the elapsed time of the muzzle burst soundwave out and back. You ignored the ~0.299 second initial delay to reach the taxi, and you have no idea what reflective surface(s) redirected the sound before the echo arrived at the taxi.
You do have a nice picture with circles on it though.
Also, as there was no firearm seen protruding from any window, if Paddock was the shooter, he and the firearm were inside the room. The sound of muzzle blast had to travel out through the hole in the window in a directional manner. No straight path to the taxi was available.
Which is irrelevant for the purpose of measuring the elapsed time between the initial Report sound event and the corresponding Echo event at the same location, at the bottom of the wall directly beneath the shooter.
Explain the difference between the Echos observed in Burst A and Burst B.
The shooter is in the same position. The taxi is in the same position. The "reflective surfaces" haven't moved. And the surface of the ground, along which the report shockwave radiated back from SOMEWHERE (probably closely relative to the aiming point), hasn't moved either.
[VxH #117] The ECHO observed and discussed in the "TEST FOR ECHO" meme is not the sound of bullet impact - it is the reflected report.
[nolu chan #121] The reportof what, reflected from what surface?
[VxH #123] Explain the difference between the Echos observed in Burst A and Burst B.
The question was,
The reportof what, reflected from what surface?
I am not interested in your evasive non-answering invitations to a snipe hunt.
If you do not know what the report was, or you do not know what it reflected from, say so. In such case, your times are meaningless for your chosen calculations.
Which is irrelevant for the purpose of measuring the elapsed time between the initial Report sound event and the corresponding Echo event at the same location
Which is irrelevant unless you had a microphone at the location of the muzzle blast, not 338+ feet away.
At ~.299s the sound reached the taxi. Also at .299s the sound had traveled 338 feet toward whatever reflective surface it found in the distance.
As the taxi is not at the location of the muzzle blast initiation, and your nonsense does not meet the conditions of the study which stipulated a microphone a few centimeters from the muzzle. The taxi was over 10,000 centimeters away.
What would the Elapsed time between the Last Report sound event and the Last Bullet sound event be....
It would be a positive number expression of time.
On your spreadsheet chartoon, notice that you calculate T = Tb - Ts.
You calculate elapsed time as the time it took the bullet to travel, minus the time it took the sound to travel.
The correct formula should be T = Ts Tb = d/Vs d/Vb.
As the bullet is supersonic, and sound is a constant, the sound would travel 400 yards in 1.06s and the bullet would travel in less than 1.06s. Subtracting 1.06 from a smaller number will always yield a negative number.
At 1200 feet, you calculate Tb as 0.448578s, and Ts as 1.062s and calculate the T as -0.6126, negative 0.6126 seconds. The average donkey could recognize that something is wrong when the result is negative time.
Just what do you think happens in negative 0.6126 seconds?
You could at least recognize that if you get a negative number, you have stated the required formula backwards, and you proceeded to perform the calculation backwards, and present the bass ackwards result of your misunderstanding of the study you looked at.
Moreover, while you state backwards that T = Tb - Ts, your spreadsheet never defines what T is supposed to represent. Negative 0.6126 is the time of what? What is the significance of this negative 0.6126 seconds (other than to demonstrate you did not understand the reference study)?
your spreadsheet never defines what T is supposed to represent.
T is the absolute value of the difference between Tb and Ts -- which corresponds to the elapsed time between T1 and T2 that is OBSERVED in the audio recording's amplitude graph.
It is that correspondence that is then used to find the range - which was generated from the ballistic data for intervals of 75 feet.
If the guy "dressed like police" was a shooter as alleged - the Elapsed Time between Bullet Impact sound events and Muzzle Report sound events would be much nearer to zero than what the audio shows.
I think everyone wants to grab the mantle of science for themselves and deride each other as kooks. Which may be mostly true.
OTOH, the official investigation is so miserably bad that you can't blame people for making up their own explanations when the FBI has botched it this badly.
The difference in time, 0.6126, is an ABSOLUTE value. Sign is irrelevant.
It is relevant when calculated and displayed on a spreadsheet. You explicitly calculated for and displayed the negative value. Had you calculated for an absolute value, a negative value would not appear. If your formula in the cell does not say it is an absolute value, you do not produce an absolute value.
You're not even reading from the relevant part of the paper - where the microphone adjacent to the victim scenario is discussed.
No, I read the correct part.
The formula is correct for a supersonic bullet only if the value is explicitly expressed as an absolute. Otherwise, the correct value is derived by changing the formula. Either will work. You did neither and derived negative times and published them that way.
Amicrophone was placed a few centimeters from the muzzleto record both the muzzle blast and the sound of the bullet hitting the deer. The time recorded between the muzzle blast and bullet striking the target represents the sum of the bullet time of flight (tb) and the time for the sound to return to the microphone from the target (ts), t = ts + tb = d/Vs + d/Vb
nolu chan
style: initial; text-decoration-color: initial"> posted on 2017-10-25 16:15:25 ET
And this is the correct section of the paper that deals with amicrophone AT THE TARGET, the scenario where the "shooter dressed as police" video in question was taken.
>>The formula is correct for a supersonic bullet only if the value is explicitly expressed as an absolute
The formula is fine just the way the authors of the paper wrote it. The negative time is perfectly acceptable IF you actually understand what the value and chart are saying:
The sound of the Report (Ts) event was recorded 0.6126 seconds after Tb and that time differential corresponds to a distance of 1200 ft from the shooter.
I think everyone wants to grab the mantle of science for themselves and deride each other as kooks. Which may be mostly true.
This is a good example of why Jefferson wanted WE common people educated. We're not supposed to be waiting for government "experts" to give us our opinions.
"... finally, that truth is great and will prevail if left to herself, that she is the proper and sufficient antagonist to error, and has nothing to fear from the conflict, unless by human interposition disarmed of her natural weapons, free argument and debate, errors ceasing to be dangerous when it is permitted freely to contradict them. "
"I HAVE SWORN UPON THE ALTAR OF GOD ETERNAL HOSTILITY TO EVERY FORM OF TYRANNY OVER THE MIND OF MAN" --Thomas Jefferson, 1786
I've always thought it likely that Jefferson's first objection to modern American government would be to the monument they built in his memory. He just wasn't that kind of guy.
I think that famous personalities in history could only speak to their own times. We like to imagine or pretend that they were some wise sages, imparting timeless wisdom for the ages, blah-blah-blah, insert three fingers and think deep thoughts, etc.
The truth is that the great men of history were creatures of their own times and only capable of speaking to the great issues of their times. And placing them on pedestals and trying to pretend that they were speaking to the issues of our time is just laziness or political hackery.
You might just as well start asking WWJT (What Would Jesus Tweet?). Well, obiously, Jesus wouldn't tweet anything and he wouldn't even imagine it. And if he could imagine it, he wouldn't bother to tweet.
I've always thought it likely that Jefferson's first objection to modern American government would be to the monument they built in his memory.
Have you ever been there?
It's not the man/statue that's being memorialized so much as the foundational American ideals for which there are trail-heads on each of the four walls.
TRUTH IS GREAT AND WILL PREVAIL.
People who don't understand Science will be bamboozled by those who do, or worse.
#140. To: Tooconservative, A K A Stone (#138)(Edited)
The difference in time between the Bullet sound event and the Muzzle Report sound event corresponds to a shooter distance of approximately 1350 feet away.
Is the guy dressed like a policeman 1350 feet away?
NO.
So the claim of the video subject of this thread, that "shooter dressed as police" - is DEBUNKED.
So the claim of the video subject of this thread, that "shooter dressed as police" - is DEBUNKED.
I never grasped why they thought there was any factual basis for this claim to begin with.
It just seemed like Kookbait to me, beginning to end. It was intended to appeal to the kooks and make some money for the con-men who created it when the kooks kept clicking on and reposting their kookery around the internet but especially on Fakebook and Twit-ter.
They have a need for their kookery. It is integral to their worldview, to their opinion of themselves and their denigrating opinions of others.
They start jonesing for a kookery within a few hours of any major tragedy. It happens over and over. 9/11, Newtown, Boston marathon, Vegas massacre, you name it. It is a very consistent pattern. It's a noxious kind of neurotic behavior.
Bring me . . . a Kookery!
And the wailing and gnashing of teeth if someone points out they are actual kooks ... oy vey.
A microphone was placed a few centimeters from the muzzle to record both the muzzle blast and the sound of the bullet hitting the deer. The time recorded between the muzzle blast and bullet striking the target represents the sum of the bullet time of flight (tb) and the time for the sound to return to the microphone from the target (ts), t = ts + tb = d/Vs + d/Vb
Regarding my initial meme "TEST FOR ECHO" -- Balistic data is NOT required to determine the total distance sound traveling from, and echoing back to, the ORIGIN point which is essentially where the Taxi driver was.
The taxi was hardly at or near the origin point. It was 338+ feet away. The study placed a microphone "a few centimers" from the muzzle, not 10,302+ centimeters away.
The taxi was 338 feet down, some distance out from the building. Even if directly opposite the taxi, the muzzle had to travel 338+ feet to get to the taxi. That still take 0.299 seconds for the muzzle blast to reach the taxi from 338 feet.
Adjusting for your cited claim (at #118) that NYT reporting "suggests that Paddock was positioned directly above the camera at this point," with the taxi directly below the window, your blather has not materially changed the problem with your chartoon. The taxi microphone was not a few centimeters from the muzzle, it was over 338 feet away.
Yeah, you make believe that the sounds recorded in the taxi can yield an accurate measurement of distance.
The problem, of course, is related in your reference study.
Using Sound of Target Impact for Acoustic Reconstructions of Shooting Events
At page 2:
A microphone was placed a few centimeters from the muzzle to record both the muzzle blast and the sound of the bullet hitting the deer. The time recorded between the muzzle blast and bullet striking the target represents the sum of the bullet time of flight (tb) and the time for the sound to return to the microphone from the target (ts),
t = ts + tb = d/Vs + d/Vb
where d is the target distance, Vs is the velocity of sound, and Vb is the average bullet velocity over the distance.
At page 5:
These results show that it is possible to use an audio recording of a shooting event to accurately determine the distance between the target and the shooter. In cases where the location of the microphone is different, the mathematical details are different, but the ideas are the same.
At page 6:
A significant weakness in the study is the placement of the microphone near the muzzle of the gun, an unlikely location in most forensic cases....
Your recording is at a taxi over 338 feet away from the muzzle. You can do all the calculations you desire and the microphone will be no closer to the muzzle. The muzzle was likely around the corner, about 338 feet up, and some angular distance away from the microphone in the taxi.
The taxi did not pick up the sounds of the bullets striking people on the ground over 1200 feet away. The muzzle blast echoed back, but you do not know where from, or what path it took to the taxi at ground level.
A taxi recording indicates the muzzle blast with a delay by the time the sound took to reach the taxi, about .299 seconds at 338 feet. During that delay, the muzzle blast is on its way to some reflective surface which redirects the sound by some route to the taxi at ground level.
The elapsed time at the 338+ foot distant taxi is not the elapsed time of the muzzle burst soundwave out and back. You ignored the ~0.299 second initial delay to reach the taxi, and you have no idea what reflective surface(s) redirected the sound before the echo arrived at the taxi.
You do have a nice picture with circles on it though.
Also, as there was no firearm seen protruding from any window, if Paddock was the shooter, he and the firearm were inside the room. The sound of muzzle blast had to travel out through the hole in the window in a directional manner. No straight path to the taxi was available.
>>How many times did #120 explicitly say { blah blah blah }
You might want to rethink the value of quoting yourself to "prove" what someone else said. Doesn't seem to be working very well for you.
The Taxi Video applies to The Test for ECHO meme - not to the video/audio being discussed in this thread which asserts that "shooter dressed as police".
That "shooter dressed as police" ASSertion is CLEARLY refuted by the audio data.
Audio data that I've analysed using the correct forumula - which works just fine without your tweakage.
Why do you keep posting this chartoon when all your data is not only wrong, but farcical? The only things you proved is that you do not know how to calculate the average velocity of an imaginary bullet and you are hopeless at spreadsheets. Your entertainment value as a useful idiot is over for now, and you will never figure it out without more help. Help is on the way, grasshopper.
Columns 1, 2, and 3 are direct entry of data generated by entering imaginary data into a generator at http://www.shooterscalculator.com/. I replicated the data taken from the calculator with My BB's. If I input initial velocity as 3240 fps, and other data, and call it My BB's, I can show a chart for magical bbs.
The Shooters Calculator only provides a result based on user input. It does not present a spreadsheet with the formulas to generate the data. The data from the Calculator can be cut and pasted into a spreadsheet, or entered by direct entry; this produces data in the cells, but no spreadsheet formulas in the cells. The chart states the speed of sound as 1130 feet per second (fps).
The remaining 4 columns, (4, 5, 6, 7) were generated by VxH.
Column 6 uses 1130.8 fps to calculate the time for sound to travel the distance stated in Column 1.
Column 4 is labeled as (Avg V) Vb. This column purports to present the average velocity of the bullet to cover the distance for the row it is in. All of the data in this column is epically wrong as the methodology of calculation is absurdly wrong.
To calculate the average velocity of the bullet, divide distance by time.
Instead of this, a personal misbegotten formula was used. Probably a pocket calculator for each cell in Column 4 was used to perform the calculations, and the data was directly entered into the cells by hand.
For the first two data rows, sum 3240 and 3163 and divide by 2. 6403/2 yields the 3201 in Column 4.
For the first three data rows, sum 3240+3163+3088 for 9491. 9491 / 3 yields the 3163.6667 in Column 4.
And so on, and so forth. All the calculated Column 4 data (average Vb), is garbage.
The chosen methodology was to sum the velocity given for each distance, and divide by the number of elements summed. This produces nonsensical data.
Example: You drive a car 100 miles at 80 mph. You drive another 100 miles at 20 mph. With this bogus methodology, 80 + 20 = 100, divide by 2, and your average velocity was 50 mph. Not.
In the real world, you drove 100/80 or 1.25 hours at 80 mph. You drove 100/20 or 5 hours at 20 mph. And you drove 200 miles in 6.25 hours. Your average speed was 200/6.25, or 32 mph.
Column 4, in addition to using an absurd methodology for its calculations, also incorporates two summing errors for the velocities taken from Column 3, at 900 feet and 1275 ft. In each case, the actual sum was 1 less than that calculated.
Spreadsheet formulas are not prone to fat finger syndrome, and do not make such errors, but someone with a pocket calculator or pen and paper does. The data was typed in after external calculation.
Where you calculate 2367.5926 average Vb at 1950 feet, 1950/1.211933 (the velocity of the bullet in Column 5), it yields 1608.9998 fps, remarkably close to the 1609 in Column 3. But then, the elapsed time in Column 2 is 0.86, not 1.21933. It is a conundrum how the bullet traveled for 1.21933 seconds in an elapsed time of 0.86 seconds.
Of course, when you use Column 1 1950 ft and Column 3 1609 fps to derive the time of flight, the formula is d/Vb, and Vb is the Average Velocity.
The bullet will travel 1905 feet distance (Col 1) in 0.86 sec time (Col 2) in 1905/0.86 or 2267.4418 average Vb. Stated in your headnote is Tb is d/Vb.
It is noteworthy that you used Column 3 as the "average" velocity of the bullet in order to derive the other average velocity of the bullet in Column 4.
Column 5 (Tb) incorporates the garbage data from Column 4 into its calculations, and all the resulting calculated data is wrong. GIGO.
Column 7 (T = Tb Ts) incorporates the garbage data from Column 5 and all the calculated data is wrong. GIGO.
The chart is multicolor and pretty, but the data for the imaginary bullet is demonstrably wrong in every column you created, except for column 6 where you succeeded in dividing the distance by 1130.8.
BTW = The Elapsed time between T1 and T2 0.689655 is quite quite sufficient for debunking the title of the video "shooter dressed as police".
Even without the ballistic data (which is calculated correctly for the parameters entered) - the difference between the bullet sound event and the report sound event puts the distance of the shooter at least 784 feet.
Is the guy "dreesed as police" 784 feet away? NOPE.
To calculate the average velocity of the bullet, divide distance by time.
Psst.
Please tell the class why, using your calculation, at 75 ft, the bullet has ACCELERATED to 3750fps, decerates to 3000fps at 150 seconds... and then accelerates to 3214fps at 225 feet... etc accelerating and decelerating and accelerating.
Is it a magic bullet?
The time in the chart rendered by the ballistic calculator only has 2 decimals of precision.
Calculating the average per the reported velocity is thus more accurate.
inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR:
rgb(255,255,255);
TEXT-INDENT: 0px; font-variant-ligatures: normal; font-
variant-caps: normal; -
webkit-text-stroke-width: 0px; text-decoration-
style: initial; text-decoration-
color: initial">>>Question my analysis of how you made a botch of the Average Bullet Velocity.
color: initial">LOL. OK - please tell the class why the bullet accelerates / decelerates / accelerates repeatedly when your "analysis" is applied?
The time in the chart rendered by the ballistic calculator only has 2 decimals of precision.
Calculating the average per the reported velocity is thus more accurate.
[Vxh #148] Even without the ballistic data (which is calculated correctly for the parameters entered)
- - - - - - - - - -
[VxH #149] Please tell the class why, using your calculation, at 75 ft, the bullet has ACCELERATED to 3750fps, decerates to 3000fps at 150 seconds... and then accelerates to 3214fps at 225 feet... etc accelerating and decelerating and accelerating. Is it a magic bullet?
[VxH #151] Calculating the average per the reported velocity is thus more accurate.
More accurate is to divide the distance by the velocity and get the time to more decimal places and eliminate the rounding error. Your bullshit methodology of summing velocities and dividing does not work. It is bullshit.
The stupid... it hurts!
The chart results are based on the data you entered.
As I demonstratred, the same data entered for My BB's produces a chart with the same data for BB's.
If the chart correctly calculated the ballistic data for the parameters you entered,
Come on. Question my analysis of how you made a botch of the Average Bullet Velocity. Give us your methodology and formula.
Why were all your calculations wrong except for distance divided by time?
The data which you input did not come from any real life ammunition, you just entered stuff, as I did for My BB's. I just entered the same stuff you did, proving my bb's have an initial Vel[x+y] of 3240 fps. My BB's perform precisely as do your imaginary cartridge. Are you saying the ballistics chart you used produced invalid results?
If the chart results are valid, please tell the class why the chart indicates the bullet traveled 75 ft. in 0.02 seconds and that indicates average velocity d/time of 750/.02 = 3750 fps.
It's your data. If the ballistics chart calculated correctly, you should understand the chart you presented, and be able to explain the results given.
Do you think you are entitled to just use a nonsense formula which produces nosense results because you do not understand the chart data that you selected and presented?
The note at the bottom of the chart indicates:
Keep in mind this is an approximation....
Of course, the time of 0.02 could represent a figure rounded to two decimal places for presentation, and actually represent anything from 0.0150 to 0.0249.
75 feet divided by Vel[x] 3239 75/3239 feet, taken to six decimal places gives 0.0231552 seconds bullet travel time. Hot damn, it's within the rounding error.
At Vel[x+y] 3240 feet per second, and 75 feet distance, the time to six decimal places would be 0.0231481 seconds bullet travel time and hot damn, that's within the rounding error too.
Thank you, Lord.
At my #108 I asked,
As for column 3, "Vel[x+y] (ft/s)", you seem to have forgotten to give any definition of x or y on your chart.
That question met with resounding crickets.
A mystery, wrapped in an enigma, hidden by a conundrum, is why, at 75 feet, the chart indicates Vel(x) = 3239, Vel (y) = 5.70, and Vel[x+y] = 3240. Whatever can that strange arithmetic be?
You could have chosen to display Vel[x] or Vel[y], or Vel[x+y]. Why did you choose to display Vel[x+y] rather than say, Vel[x]? What is Vel[x], Vel[y], and Vel[x+y]?
divide the distance by the velocity and get the time to more decimal places and eliminate the rounding error.
LOL.
So you're going to drive 99 miles at 2mph, then drive and 1 mile at 100mph.
You're going to divide 100 miles by what 100mph?
Here are the values of Nolu- Time calculated with your d/v brainstorm:
Ooops!
Congratulations! You "fixed" the rounding of 0.86 by transforming it into 1.2119328776 are you sure that works?
"Vel[x+y] (ft/s)", you seem to have forgotten to give any definition of x or y on your chart.
LOL. I know what they mean on the Ballistic calculator. Don't you?
Hint: They're Vectors.
And speaking of Vectors: If we treated each 75 ft segment as a vector and then calculated time as a function of the relationship between 75ft and the difference between {Vn..Vn+1}... that might work a little better than your simple d/v idea.