Contact Information:

Georg Hothaus

Waffen Holthaus

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Ballistic Business Card

The idea behind the Ballistic Business Card is to give the card receiver something more than just contact information.

Usually business cards are discarded or stored away and forgotten very quickly. If the card has more use, it is more likely to keep it around and have the contact information present and in memory. A classic example are cards with calendars or measuring tape.

For long range shooters having ballistic range cards is obviously useful. So we put together a comprehensive range card with some additional tools that hopefully help the shooter and also keep our contact information handy.

The contact information part of the card is as small as possible through the use of a QR-Code with just the name, company and website all combined in the email address. The QR-Code - which leads to this website - allows the business card to always have current contact information, as we can change the information on the website after the card is already printed and handed out.

In the following sections is a description on the use of the Ballistic Business Card.

Although the ballistic information on the card is comprehensive, it is still limited to the size of the card and the nature of making ballistic calculations easy without a ballistic calculator. Therefore the firing solutions made with the this card are not as precise as computer assisted calculations.

It is recommended to make all the needed calculations on a different medium - piece of paper or Excel chart - and write the information on the card after all data is correctly compiled.
Although most type of pens can be used to write on the card, pencils are easy to erase and allow changes of the information afterwards.

MilDot Centimetre Scale

The centimetre scale comes in handy to measure group size, deviation and scope build height.

The MilDot scale corresponds to the centimetre scale with 1mrad = 1cm. This makes the millimetre subdivision a 0.1mrad scale compared to the MilDot and helps to find subdivisions on the reticle.

On the left side of the MilDot are dotted lines with half mrad spacing, to write distances for holdovers.

AQRAS - Advanced Quick Ranging Scale

The AQRAS by Minox is a unique new tool for measuring target distance for any known target size (height and width) with just one measurement and one easy multiplication.

It is integrated in the MR reticles of the Minox ZP Professional Rifle Scopes. For more information visit our Minox ZP product page.

How it works:

Put the target on the base line and read the value from the scale.

Multiply the scale number with the known target size in centimetre (cm) to get the corresponding target distance in metre (m):

Target Size (cm) x scale value = distance (m)

CoSine° - Scale

The CoSine°-scale helps to measure angle, clock face 'time' and the corresponding Sine and Cosine.

On the outside of the radius lines show angle with 15° spacing. The long lines represent 30° increments which correspond to the full hours on a clock face. The short lines are 15° apart from the long lines and correspond to the half hours on a clock face.

To find the angle or 'time' between two points, point one of the thick MilDot lines in the direction of one point and read of the angle/'time' for the second point.
For incline fire the two points to measure are the Target and the Horizone (0° incline).
For wind value the two points to measure are the Target and the Wind Direction.

Within the radius there are white and grey slices. These represent the Sine or Cosine values for the corresponding angle, rounded to 10% or 0.1 increments. The even numbers in the white slices can be read as percent(%) (for example 80%) or as Sine/Cosine value (for example 0.80). The grey slices in between represent the odd Sine/Cosine values (for example 90% or 0.90).

The upper MilDot line represents the base line for measuring the Cosine, for example when calculating incline fire solution. It is therefore marked with "COS" and "DRP", whereby DRP stands for the Bullet Drop, which has the be adjusted for incline fire.

The right MilDot line represents the base line for measuring the Sine, for example when calculating wind values. It is therefore marked with "SIN" and "WND", whereby WND stands for Wind.

As the radius does not continue in the lower left sector (because of the QR Code), it is possible to use the lower MilDot line as base line for COS/DRP, respectively the left MilDot line for SIN/WND to get the measurement.

Ballistic Ammo/Gun Data

The data section allows to note various information of the ammo and gun.

ID: = Description to identify the used ammo, load and gun for the ballistic data. It should be short and precise to allow easy identification.

Zero = Range at which the scope is zeroed, e.g. "100m"

Tmp = Load temperature when zeroed, e.g. "20°C"
This is used as the baseline when adjusting bullet drop and wind deviation for changes in muzzle velocity because of load temperature change.

DA = Density Altitude when zeroed, e.g. "500m"
This is used as the baseline when adjusting bullet drop and wind deviation for changes in air density.
Density Altitude represents a combination of air pressure and temperature and is shown as a value of height above sea level. The drag on the bullet in flight corresponds to the air density. Anemometer like the Kestrel 4000 series can directly measure Density Altitude and most modern ballistic calculators can use DA to calculate bullet flight. DA is also easier to conceivable in practical use and allows easier adjustment of firing solutions than with pressure and temperature separate.

Vo = muzzle velocity when zeroed, e.g. "850m/s"

BC = Ballistic Coefficient of the bullet used, e.g. "0.243 G7"

SG = Miller Stability Factor, e.g. "1.7"
A bullet in flight should have atleast a SG of 1.0. Below that it gets instable, which results deviation from the flight path.
Because SG is dependent on the muzzle velocity, which can change because of load temperature, it is commonly recommended to have a vaule of SG = 1.4 to be save when muzzle velocity gets lower in colder temperature. New research by Bryan Litz shows that a SG above 1.5 should be intended, as the BC of bullets in flight maximizes at this value.

BH = Build Height of the scope above the gun barrel, e.g. "5cm"
Useful when making shots at extrem short ranges, were the bullet is still below the line of sight.
Also needed to calculate canting errors, when shooting with wilful canting of the gun.

EG = Elevation of the gun to the line of sight when at zero range, e.g. "1.3mrad"
Needed to calculate canting errors, when shooting with wilful canting of the gun.

Offest = Deviation from Zero at zero range, e.g. "0.3U 0.2R"
Main use can be to note deviation when using suppressor.
Can also be used when using different loads or calibres in the same gun system without re-zeroing the scope.

ΔTmp - DRP% - WND% = Changes in bullet drop and wind deviation corresponding to load temperature changes.
Description of use in separate section.

DAwnd% = Change in wind deviation because of change in air density.
Description of use in separate section.

Fmagnus = Magnus effect resulting in deviation because of wind deviation.
Description of use in separate section.

Latitude = Latitude when zeroed
Important for calculation of Coreolis Effect.

DRP% - WNDclk = Coreolis Effect.
Description of use in separate section.

Range Card

On the Range Card all the bullet flight information can be noted for 20 different ranges.

RNG = Target Range

PTH = Bullet Path
Is the sight correction needed for target impact at range because of bullet drop. Should be noted in Clicks, mrad/mil or MOA.

DRP = Bullet Drop
Is the drop of the bullet from the barrel at range. Is needed to calculate deviations for incline fire, DA and load temperature changes.

DA = horizontal Density Altitude change
Should be noted as height above sea level.

WND = Wind Deviation
Is the sight correction needed for target impact at range because of wind deviation.

SPN = Spin Drift
Additional horizontal deviation because of gyroscopic spin drift at range. Deviation is to the side corresponding to barrel twist. E.g. right hand twist = Bullet move to the right = has to be corrected to the left.

TOF = Time of Flight
Needed for Coreolis Effect and Lead calculation.

Getting Basic Data

To get the basic ballistic data about the gun and load, information is needed and basic ballistic calculations have to be made.

ID
Should be noted as: Gun/Calibre - Bullet Type - Weight
e.g.: ".308W SST 165grs".

Zero = selected zero range - e.g. "100m"
Vo = muzzle velocity when zeroed - e.g. "850m/s".
BC = BC of the bullet used - e.g. ".560 G1".
BH = scope build height above barrel - e.g. "5cm".
Offset = Offset from Zero if needed - e.g. "U0.3".

RNG = range / target distance
Range increments should start with Zero range. Can be incremented in any steps needed (e.g. 100m, 50m, 25m) or can be corresponding to full mrad, MOA or Click values.

PTH = bullet path
Can be directly calculated with most ballistic calculators. Recommended free programm: JBM Ballistics 'Trajectory'.
Should be noted as Click, mrad or MOA values.

WND = Wind Deviation
Can be directly calculated with most ballistic calculators. Recommended free programm: JBM Ballistics 'Trajectory' when deselecting 'Windage Correction for Zero Range'.
Should be noted as Click, mrad or MOA value. Should be calculated to a specific wind speed at full / 90° value, e.g. for 1m/s or 10m/s (which is =10x 1m/s).

TOF = Time of Flight
Can be directly calculated with most ballistic calculators. Recommended free programm: JBM Ballistics 'Trajectory'.

Getting Additional Data

Tmp = Zero Load Temperature
The easiest way is the get the load/ammo to ambient temperature and measure it with a thermometer like the Kestrel Wind Meters and noted e.g. "20°C".

DA = Zero Density Altitude
Can be measured with e.g. the Kestrel 4000s Series of Wind Meters. Should be noted as height above sea level, e.g. "500m".

SG = Miller Stability
Can be calculated with JBM Ballistics 'Stability'.

EG = Gun Elevation when zeroed
When calculating the PTH - Bullet Path JBM Ballistics 'Trajectory' will calculated Elevation in output data.
Should be noted a Click, mrad or MOA value.

Fmagnus = Aerodynamic Jump
Formula for calculating the Magnus Force Effect on the bullet for horizontal wind deviation:

Fmagnus = (0.01×SG - 0.0024×Bullet Length/Bullet Diameter + 0.032)×0.651

The calculated value is the vertical deviation in mRad per m/s of wind speed value.

Depending on direction of rifle twist the Aerodynamic Jump is up or down. For right hand twists it is down for wind from the left and up for wind from the right of the flght path.

Latitude can be found in a map or with GPS.

DRP = Bullet Drop
Bullet drop can be calculated using JBM Ballistics 'Trajectory' when setting the 'Sight Height' to zero and deselect 'Elevation Correction for Zero Range'.
This will calculate true bullet drop in the "Drop" column of the program.

SPN = Spin Drift
Can be calculated with JBM Ballistics 'Trajectory -- Drift' when setting wind speed to zero.
Should be noted in Click, mrad or MOA values with direction to compensate, e.g. "1L".

Density Altitude Changes

Changes in Air Density result in a change of drag on the bullet in flight. Air Density changes with air temperature, pressure and humidity.

Density Altitude (DA) is a measurement of Air Density by corresponding a height above sea level of a standard atmosphere to the actual atmosphere. The actual atmosphere then is equal to the standard atmosphere at a certain height of DA.

DA therefore includes temperature, pressure and humidity in one easy to comprehend number, as shooters know the higher above sea level you shoot the more flat the trajectory gets because of lower air density.

Density Altitude can be measured by weather stations like the Kestrel 4000s Series or calculated by using Density Altitude tables and can be used in some advanced ballistic calculators like JBM Ballistics.

A change in drag on the bullet results in different changes for vertical (bullet drop) and horizontal (wind deviation). Therefore different compensations have to be made for each directions. These compensation methods below are not precise, but easy to use in the field without computer assistance.

DA - vertical compensation:

A change in DA results in a range depending change in bullet drop. Therefore to find the change at range the bullet drop - DRP - has to be calculated for different DA values.

The bullet drop can be calculated using JBM Ballistics 'Trajectory', by setting the 'Sight Height' to zero and deselect 'Elevation Correction for Zero Range'. To set a specific DA in the calculator 'Std. Atmosphere at Altitude' has to be checked and the DA height above sea level put in the 'Altitude' field. The fields for 'Temperature', 'Pressure' and 'Humidity' are switched off and not needed now.

By calculating the bullet drop for different settings of DA = 'Altitude' it is possible to calculate the changes.

It is recommended to use an Excel chart to compile the data and make the calculation.

Useful change in DA could be 1000m difference.

For each distance it is possible to calculate how many mRad, MOA or click is needed for a specific change in DA (e.g. 1000m steps):

DA = (Drop at lower altitude) - (Drop at higher altitude)

It is also possible to calculate how much change in DA is needed for each mRad, MOA or click:

DA = 1000m / ((Drop at lower altitude) - (Drop at higher altitude))

The calculated values can be noted in the range chart on the Ballistic Business Card in the 'DA' column.

To use DA in the field reduce the PTH and/or DRP value by the DA change for higher than zeroed Density Altitudes and then add the DA change to the PTH and/or DRP for lower than zeroed Density Altitudes.

DAwnd% - horizontal compensation:

A change in DA results in an approximated percentage change in wind deviation. Therefore to find the change in percent of wind deviation has to be calculated for different values of DA.

The wind deviation can be calculated using JBM Ballistics 'Trajectory', by checking 'Std. Atmosphere at Altitude' and the DA height above sea level put in the 'Altitude' field. The fields for 'Temperature', 'Pressure' and 'Humidity' are switched off and not needed now.

It is recommended to use an Excel chart to compile the data and make the calculation.

Useful change in DA could be 1000m difference.

For each distance it is possible to calculate the percentage of change in wind deviation per change in DA:

DAwnd% = (1 - (Wind deviation at higher altitude) / (Wind devitation at lower altitude)) / 100

The percentage per range differ slightly. One has to make an educated guess which average percentage to use.

The estimated percentage can be noted in the info section of the Ballistic Business Card at 'DAwnd%'.

To use DAwnd% in the field reduce the WND value by the DAwnd% percentage for higher than zeroed Density Altitudes and add to the WND value by the DAwnd% percentage for lower than zeroed Density Altitudes.

Load Temperature Changes

A change in powder temperature results in a change in muzzle velocity, which leads to a different bullet drop and wind deviation. Colder powder results in more drop and more wind deviation. Warmer powder results in less drop and less wind deviation.

Most powders show a linear change in muzzle velocity with temperature change. A change in muzzle velocity shows a almost linear change in bullet drop and approximately linear change in wind deviation. It is therefore possible to calculate an approximated percentage of bullet drop and wind deviation change for a change in powder temperature. These compensation methods are not precise, but easy to use in the field without computer assistance.

To measure the powder temperature directly is not easy, as the powder is in the case which is in the chamber of the gun. One solution is to measure the ambient temperature after the gun and ammo in it had time to adjust to that temperature. The powder temperature will not be the ambient temperature, but as the change in muzzle velocity is linear only the relative temperature change is needed not the absolute value.

To get the relative change in muzzle velocity per change in temperature, the muzzle velocity has to be measured at different temperatures.

Another possible way to get the relative changes is to use a reloading software like "QuickLoad", which has a powder database that allows changes to powder temperature and calculates muzzle velocity.

ΔTmp:

The first determination to make is the relative change in temperature for which the percentage change in drop and wind will be calculated, e.g. 10°C. This ΔTmp can be noted in the info section of the Ballistic Business Card.

DRP%:

To get the percentage for change in bullet drop per ΔTmp first to differnet muzzle velocities have to be determined. With those Vo values the two bullet drops can be calculated using JBM Ballistics 'Trajectory' when setting the 'Sight Height' to zero and deselect 'Elevation Correction for Zero Range'. This will calculate true bullet drop in the "Drop" column of the program.

For each range the percentage can now be calculated by subtracting one drop value from the other and then divide it by the zeroed DRP:
DRP% = ((zeroedDRP) - (ΔTmpDRP))×100 / (zeroedDRP)

The percentage per range differ slightly. One has to make an educated guess which average percentage to use.

The DRP% can be noted in the info section of the Ballistic Business Card.

In the field this percentage is the amount of DRP by which to change the calculated PTH. In higher than zeroed temperature the change has to be subtracted from the PTH, in lower temperature it has to be added to PTH.

WND%:

To get the percentage for change in wind deviation per ΔTmp first to different muzzle velocities have to be determined. With those Vo values the corresponding wind deviation can be calculated using JBM Ballistics 'Trajectory'.

For each range the percentage can now be calculated by subtracting one wind deviation from the other and then divide it by the zeroed wind deviation:
WND% = ((zeroedWND) - (ΔTmpWND))×100 / (zeroedWND)

The percentage per range differ slightly. One has to make an educated guess which average percentage to use.

The WND% can be noted in the info section of the Ballistic Business Card.

In the field this percentage is the the amount of WND by which to change the calculated WND:
In higher than zeroed temperature the change has to be subtracted from the WND, in lower temperature it has to be added to WND.

Coreolis Effect

The Coreolis Effect results from the movement of the earth's surface during the flight time of the bullet. It results in the target 'moving' out of the way of the flight path of the bullet. From the shooter point of view, who assumes that the target does not move, it looks like the bullet path moves away from the target. This deviation can be calculated for the vertical and horizontal movement. It has to be noted that the bullet deviation because of the Coreolis Effect is very small and should only be compensated at extrem long range and long time of flights.

DRP%:

The vertical deviation, which affects the bullet drop, is calculated as:
DRP% = (RNG / TOF × sin(Azimuth)) × (2Ω/g × cos(Latitude))

With Ω=0.00007292rad/s and g=9.81m/s the term becomes:
DRP% = (RNG / TOF × sin(Azimuth)) × (0.000014866 × cos(Latitude))

With the Latitude known the second part of the term can be calculated and noted on the Ballistic Business Card behind the first part of the term there.

When calculating a firing solution in the field, this number has to be multiplied with the Sine of the Azimuth (compass heading to target) and the RNG / TOF. The result can be positive or negative and is the percentage by which the Drop of the Bullet - DRP - is changed.

This change has to be added to the bullet path - PTH:
Vertical firing solution = PTH + (DRP×DRP%)

To find the Sine of the Azimuth the CoSine°-Scale can be used by pointing the upper MilDot-line to geographic north and reading of the value in the direction of the target.

WNDclk:

The horizontal deviation, which affects windage, is calculated as:
WNDclk = TOF × (10000Ω × sin(Latitude))

With Ω=0.00007292rad/s and the Latitude known the second part of the term can be calculated and noted on the Ballistic Business Card behind the first part of the term there:
WNDclk = TOF × (0.7292×sin(Latitude))

When calculating a firing solution in the field, this number has to be multiplied with the time of flight to the target (TOF).

The result is the horizontal deviation in mRad, whereby a positive value of WNDclk means a correction to the left and a negative value a correction to the right.

This has to be added to the horizontal firing solution:
Horizontal firing solution = WND + PTH + WNDclk

Example Range Card

The following example can give an idea how to use the Ballistic Business Card

Data is compiled as metric (m, cm), 0.1mrad Clicks, °C. WND is for 10m/s full wind.

As a experiment to show the possible precision, the following firing solution shall be calculated with the card.

Range: 1500m; Incline +30°; Density Altitude: 2500m; Powder Temperature: 0°C; Azimuth: 90°; Wind:10m/s from 60°

The vertical firing solution for PTH is calculated:

First the DRP has to be adjusted because of lower powder temperature:
DRP% = 2.9%/10°C
DRP = DRP + 2×DRP% = U211.9 + 2×2.9% = U211.9 + U12.3 = U224.2

Second the DRP has to be further adjusted for the change in Density Altitude:
DA = 12.3 clicks/1000mDA
DRP = DRP - 2×DA = U224.2 - 2×U12.3 = U199.4

Third the change to the DRP resulting from the 30° inclined line of sight has to calculated:
DRP = DRP × cos(30°) = U199.4 × 0.87 = U173.5

Finally the total change to the PTH from this is the difference between the original DRP and this adjusted DRP:
PTH = PTH - (DRPoriginal - DRPnew) = U198.8 - (U211.9 - U173.5) = U160.4

Additional changes to PTH can and should be calculated:

Because of the inclined bullet flight path the head/tail wind component can add/reduce the DRP and therefore the PTH of the bullet.

First the WND has to be adjusted because of lower powder temperature:
WND% = 2.1%/10°C
WND = WND + 2×WND% = 62.5 + 2×2.1% = 62.5 + 2.6 = 65.1

Second the WND has to be further adjusted for the change in Density Altitude:
DAwnd% = 13.3%/1000mDA
WND = WND - 2×DAwnd% = 65.1 - 2×13.3% = 65.1 - 17.3 = 47.8

Now the head wind component can be calculated with the Cosine of the wind direction:
WND = WND × cos(60°) = 47.8 × 0.5 = 23.9

Finally this head wind has to be adjusted for the incline as a component of the head wind which pushes the bullet up resulting in less DRP:
PTH = WND × sin(30°) = 23.9 × 0.5 = D12.0

Because of crosswind from the right the bullet will make a gyroscopic jump up resulting in less PTH correction needed.

First the cross wind component has to be calculated with Sine of the wind direction:
Cross Wind = Wind Speed × sin(60°) = 10m/s × 0.87 = 8.7m/s

The gyroscopic jump is 0.26 Clicks per 1m/s:
Fmagnus = 0.26 × 8.7 = D2.3

Finally the gyroscopic jump has to be adjusted for the incline of the line of sight:
Fmagnus = Fmagnus × cos(30°) = D2.3 × 0.87 = D2.0

Because of the earth's rotation the PTH has to be adjusted for the vertical Coreolis Effect.

First the percentage of vertical change in bullet drop - DRP% - has to be calculated:
DRP% = RNG×sinAZ/TOF × 0.000009152 = 1500m × sin(90°) / 2.878sec × 0.000009152 = 0.48%

The DRP has to be reduced when shooting East (90°) by DRP% after DRP has been adjusted for powder temperature and Density Altitude:
DRP% = DRP × DRP% = 199.4 × 0.48% = D1.0

Finally the vertical Coreolis Effect has to be adjusted for the incline of the line of sight:
DRP% = DRP% × cos(30°) = D1.0 × 0.87 = D0.9

To get the correct PTH for all the above effects they have to be added up:
PTH = U160.4 + D12.0 + D2.0 + D0.9 = D145.5

For comparison JBM Ballistics 'Trajectory' calculates the PTH (without Magnus and Coreolis) with U149.3 compared to the U160.4 + D12 = U148.4 of the Ballistic Business Card.

The horizontal firing solution for WND is calculated:

First the WND has to be adjusted because of lower powder temperature:
WND = WND + 2×WND% = 62.5 + 2×2.1% = 62.5 + 2.6 = 65.1

Second the WND has to be further adjusted for the change in Density Altitude:
WND = WND - 2×DAwnd% = 65.1 - 2×13.3% = 65.1 - 17.3 = 47.8

Fianlly the cross wind value has to be calculated for the wind direction coming from 60°:
(Wind coming from the right has to be compensated to the right 'R')
WND = WND × sin(60°) = 47.8 × 87% = R41.6

Additional changes to WND can and should be calculated:

Gyroscopic Spin Drift should be compensated for.

Spin Drift moves the bullet to the side of the Twist Direction and has to be compensated to the opposite side.
(Right hand twist direction moves bullet to the right and has to be compensated to the left 'L')
SPN = L4.5

Because of the earth's rotation the WND has to be adjusted for the horizontal Coreolis Effect.

In the northern hemisphere the Coreolis Effect will move the bullet to the right and has to be compensated to the left 'L'.
The number of CLicks to the left because of the Coreolis Effect is calculated:
WNDclk% = TOF × 0.2143 = 2.878sec × 0.2143 = L0.6

Because of the incline flight of the bullet there is a head wind component moves the bullet up. The bullet therefore will make a gyroscopic jump to the right because of this and has to be compensated to the left 'L'.

First the head wind component has to be calculated with Cosine of the wind direction:
Head Wind = Wind Speed × cos(60°) = 10m/s × 0.5 = 5m/s

Second from this head wind the cross wind component (acting upon from below) has to be calculated because of the incline:
Cross Wind = Head Wind × sin(30°) = 5m/s × 0.5 = 2.5m/s

Finally the gyroscopic jump resulting from the inclined head wind is:
Fmagnus = 0.26 × 2.5m/s = L0.7

To get the correct WND for all the above effects they have to be added up:
WND = R41.6 + L4.5 + L0.6 + L0.7 = R35.8

For comparison JBM Ballistics 'Trajectory' calculates the WND (Wind and Spin Drift only) with R37.1 compared to the R41.6 + L4.5 = R37.1 of the Ballistic Business Card.