Fun with Lab Radar Data - Initial findings on variability of BC as shot

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I could clean up the below formula but I am too lazy.

C30 = Temp (in f)
C28 = Distance between two measured velocities (expressed in yards)
E28 = Velocity 1 (fps)
E30 = Humidity%
G27 = Velocity 2 (fps)
G30 = Elevation (in ft)

(cleaned up version)

=(((((101325 * EXP(-9.80665 * 0.0289644 * (G30*0.3048)/(8.31432 * ((C30 - 32) * 5/9 + 273.15)))-E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9)/((C30 - 32) * 5/9 + 243.5))*100)/(287.05*((C30 - 32) * 5/9 + 273.15))+(E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9)/((C30 - 32) * 5/9 +243.5))*100/(461.5*((C30 - 32) * 5/9 + 273.15))))+(E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9)/((C30 - 32) * 5/9 +243.5))*100/(461.5*((C30 - 32) * 5/9 + 273.15))))*0.062428)*0.026068* C28) / ( SQRT(E28) - SQRT(G28))

-Matt
 
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I got this from chatgpt, it is much simpler but same results that match Chaingun?

how to calculate the ballistic coiefienct GA for pellets given as input V1 and V2 over a distance, answer as excel function

ChatGPT said:​


To calculate the ballistic coefficient GAG_AGA for pellets using two velocities V1V_1V1 and V2V_2V2 measured over a known distance ddd, you can use the following formula:
GA=dln⁡(V1/V2)G_A = \frac{d}{\ln(V_1 / V_2)}GA=ln(V1/V2)d
Here's how you can set this up as an Excel function:
  1. Input Data:
    • V1V_1V1: Initial velocity (in meters per second, for example) in cell A1
    • V2V_2V2: Final velocity (in meters per second) in cell A2
    • ddd: Distance over which the velocity changes, in cell A3
  2. Excel Formula:In cell A4, enter the following formula to calculate GAG_AGA:
=A3 / LN(A1 / A2)
 
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Stubbers said:
I could clean up the below formula but I am too lazy.

C30 = Temp
C28 = Distance between two measured velocities
E28 = Velocity 1
G27 = Velocity 2
G30 = Elevation

=((((((101325 * EXP(-9.80665 * 0.0289644 * (G30*0.3048)/(8.31432 * ((C30 - 32) * 5/9 + 273.15)))-E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9 + 273.15-273.15)/((C30 - 32) * 5/9 + 273.15-273.15+243.5))*100)/(287.05*((C30 - 32) * 5/9 + 273.15))+(E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9 + 273.15-273.15)/((C30 - 32) * 5/9 + 273.15-273.15+243.5))*100/(461.5*((C30 - 32) * 5/9 + 273.15))))+(E30/100*6.112*EXP((17.67*(C30 - 32) * 5/9 + 273.15-273.15)/((C30 - 32) * 5/9 + 273.15-273.15+243.5))*100/(461.5*((C30 - 32) * 5/9 + 273.15))))*0.062428)*0.026068* C28) / ( SQRT(E28) - SQRT(G28)))

-Matt
Click to expand...
It seems that a lot of the number have to do with temp correction and baro pressure. It would be easier of those numbers were factored out into separate cells. They don't change per test session and are a constant per shot string. No humidity corrections?
 
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BlackICE said:
It seems that a lot of the number have to do with temp correction and baro pressure. It would be easier of those numbers were factored out into separate cells. They don't change per test session and are a constant per shot string. No humidity corrections?
Click to expand...

Easier? You only write the formula once and then drag in excel, but again, I am too lazy and not refactoring that formula for anyone, you certainly can yourself.

No humidity correction that I am aware of. *edited I missed in my own formula where I had humidity, was rushed trying to get in the shower my bad lol

-Matt
 
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BlackICE said:
It seems that a lot of the number have to do with temp correction and baro pressure. It would be easier of those numbers were factored out into separate cells. They don't change per test session and are a constant per shot string. No humidity corrections?
Click to expand...

Also fwiw, most of that is calculating air density and converting from imperial to metric, since I am in the US and still adhere to imperial units.

Humidity is cell E30
 
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BlackICE said:
I got this from chatgpt, it is much simpler but same results that match Chaingun?

how to calculate the ballistic coiefienct GA for pellets given as input V1 and V2 over a distance, answer as excel function

ChatGPT said:​


To calculate the ballistic coefficient GAG_AGA for pellets using two velocities V1V_1V1 and V2V_2V2 measured over a known distance ddd, you can use the following formula:
GA=dln⁡(V1/V2)G_A = \frac{d}{\ln(V_1 / V_2)}GA=ln(V1/V2)d
Here's how you can set this up as an Excel function:
  1. Input Data:
    • V1V_1V1: Initial velocity (in meters per second, for example) in cell A1
    • V2V_2V2: Final velocity (in meters per second) in cell A2
    • ddd: Distance over which the velocity changes, in cell A3
  2. Excel Formula:In cell A4, enter the following formula to calculate GAG_AGA:
=A3 / LN(A1 / A2)
Click to expand...


Mmmm, you need to know the air density...

-Matt
 
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FWIW the difference from 0% humidity to 100% is only .0003 in BC, difference in 50F (50f vs 100f) is .0031, and the difference in elevation from 0 to 5000 feet is .0077, with the conditions I used which is akin to a 33.95 MKll pellet, but not 100% one as its arbitrary.

So that gives an idea how critical it is to have environmental conditions considered in this calculation.

-Matt
 
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BlackICE said:
So is your elevation number used as baro pressure correction assuming STP at sea level and then modifying pressure by setting the altitude that at stp would equal the pressure at the shooter's location?
Click to expand...

Its the same formula Chairgun uses. Test it next to Chairgun and change the pressure/temp/humidity in Chairgun or in the formula I provided, it should line up, unless I had a stroke when writing it.

Its a correction factor, nothing to do with STP because no STP values are present in the formula, it takes your density in kg/m3 converts to lbs/ft3 then again to slug/ft3.

My version calculates your air density from elevation/temp/humidity opposed to direct pressure input because, 'corrected' pressure values have to be uncorrected anyway so why not just avoid that confusion and calculate the density myself.

-Matt
 
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You still need to account for changes in bara pressure due to weather. Here is the inputs to Chairgun



1730246229160.png

1730246267175.png
 
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ChatGPT:

To calculate air density, we need the elevation, temperature, and humidity as inputs. Here’s a step-by-step outline of the approach:

Required Inputs and Constants​

  • Elevation (hhh): in feet (converted to meters).
  • Temperature (TTT): in Celsius.
  • Relative Humidity (RHRHRH): as a percentage.
  • Universal Constants: including specific gas constants for dry air and water vapor, and standard values for gravity, molar mass, and base pressure at sea level.

Formula Outline​

  1. Calculate Atmospheric Pressure at a given elevation, using the barometric formula.
P=P0×(1−L×hT0)g×MairRdry air×LP = P_0 \times \left(1 - \frac{L \times h}{T_0}\right)^{\frac{g \times M_{\text{air}}}{R_{\text{dry air}} \times L}}P=P0×(1−T0L×h)Rdry air×Lg×Mair
Where:
  • P0P_0P0 = Sea level pressure (101325 Pa)
  • hhh = Elevation in meters
  • LLL = Temperature lapse rate (0.0065 K/m)
  • T0T_0T0 = Standard temperature at sea level (288.15 K)
  • ggg = Acceleration due to gravity (9.80665 m/s²)
  • MairM_{\text{air}}Mair = Molar mass of dry air (0.0289644 kg/mol)
  1. Calculate Saturation Vapor Pressure PsatP_{\text{sat}}Psat at the given temperature (Tetens formula):
Psat=6.112×exp⁡(17.67×TT+243.5)P_{\text{sat}} = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right)Psat=6.112×exp(T+243.517.67×T)
  1. Calculate Actual Vapor Pressure PH2OP_{\text{H2O}}PH2O using relative humidity:
PH2O=RH×PsatP_{\text{H2O}} = RH \times P_{\text{sat}}PH2O=RH×Psat
  1. Calculate Partial Pressure of Dry Air PdP_dPd:
Pd=P−PH2OP_d = P - P_{\text{H2O}}Pd=P−PH2O
  1. Calculate Air Density ρ\rhoρ:
ρ=PdRdry air×T+PH2ORwater vapor×T\rho = \frac{P_d}{R_{\text{dry air}} \times T} + \frac{P_{\text{H2O}}}{R_{\text{water vapor}} \times T}ρ=Rdry air×TPd+Rwater vapor×TPH2O
Where:
  • Rdry air=287.05 J/(kg\cdotpK)R_{\text{dry air}} = 287.05 \, \text{J/(kg·K)}Rdry air=287.05J/(kg\cdotpK)
  • Rwater vapor=461.5 J/(kg\cdotpK)R_{\text{water vapor}} = 461.5 \, \text{J/(kg·K)}Rwater vapor=461.5J/(kg\cdotpK)
I’ll calculate this using example values:
  • Elevation = 5000 feet
  • Temperature = 25°C
  • Relative Humidity = 60%
The calculated air density at an elevation of 5000 feet, a temperature of 25°C, and 60% relative humidity is approximately 1.169 kg/m³.
This value incorporates the effects of temperature, elevation, and humidity on air density.
 
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BlackICE said:
It would be nice to modify it to take just one number "altitude density" Since I have a Kestrel that can give me this number instead of using many inputs.
Click to expand...

Convert your density altitude to density in slugs/ft3 and you're golden, assuming velocity in FPS and distance in yards.

slugs/ft3 * Distance / ( SQRT(V1) - SQRT(V2)

Also in the above, chatgpt miscalculated, the air density at 5000 ft 25c and 60% humidity is .9996 kg/m3.

-Matt
 
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Ask chatgpt of P0 changes (P0P_0P0 = Sea level pressure (101325 Pa)) then the calculation doesn't work acurately.

P0 is assumed but it isn't a constant.

P=P0×(1−L×hT0)g×MairRdry air×LP = P_0 \times \left(1 - \frac{L \times h}{T_0}\right)^{\frac{g \times M_{\text{air}}}{R_{\text{dry air}} \times L}}P=P0×(1−T0L×h)Rdry air×Lg×Mair
Where:
  • P0P_0P0 = Sea level pressure (101325 Pa)
  • hhh = Elevation in meters
  • LLL = Temperature lapse rate (0.0065 K/m)
  • T0T_0T0 = Standard temperature at sea level (288.15 K)
  • ggg = Acceleration due to gravity (9.80665 m/s²)
  • MairM_{\text{air}}Mair = Molar mass of dry air (0.0289644 kg/mol)
 
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