By Koaw - December, 2021
As promised from our video on optimizing play height for the drop-shot fishing rig (found here on the KN Fishing Smarts YouTube Channel), here is how to calculate the play height on a drop-shot rig.
This page is for those wishing to explore how we reached the concepts in the video. It’s more of a nerdy resource rather than one for anglers.
The KNFS Drop-Shot Simulator is for anglers to quickly calculate their play height without having to do math.
Let’s get into this.
CALCULATING PLAY HEIGHT - QUICK VERSION
WANT TO FIND: The max play height (PH) of the hook off of the bottom.
SIMPLE CALCULATION: Let’s work a bit backwards and immediately look at the drop-shot rig underwater. A triangle is created by drawing that orange dotted-line. We only need to know two variables in order to solve for our play height (PH), or the side of the triangle opposite of the angle θIA.
THE TWO VARIABLES NEEDED:
Important Angle (θIA) – The important angle is the angle created along a taught line that will remain the same anywhere along that line assuming that line stays perfectly straight. The important angle is the angle we can see when the line penetrates the water and it’ll remain the same on a flat bottom.
Tag End Length (TL) – The tag end length is the distance between the hook and the weight as they are tied on the end of the fishing line.
Click on image to enlarge.
STEP 1: We are dealing with a right triangle. We just need to use a trigonometric ratio to solve for PH. We’ll summon that good ‘ol SOHCAHTOA mnemonic and use the SOH or SIN(θ) = OPP/HYP ratio. The TE side corresponds to the hypotenuse and the PH side corresponds to the opposite side.
For our calculation, that will look like: SIN(θIA) = PH/TE
STEP 2: So if we multiply both sides by TE our play height will calculate as follows: PH = SIN(θIA) * TE
That’s easy—just plug in θIA and TE to find PH.
NOTE: Make sure your calculator is set to calculate in DEG for degrees instead of RAD for radians.
Try it out: Say you have an important angle (θIA) of 67.5 degrees and a tag end length (TE) of 1 foot. You’re play height should calculate to 0.92388 ft.
CALCULATING PLAY HEIGHT - FINDING IMPORTANT ANGLE FIRST
FINDING OUR IMPORTANT ANGLE: So let’s say we don’t know our important angle. As fishers, we’ll normally just approximate this by looking at the angle where our fishing line hits the water. However, we can calculate the important angle if we know some other variables.
Rod Angle (RA) = Rod angle is the angle we hold the rod over a parallel plane to the water level.
Rod Length (RL) = Rod length is the entire length of the rod from butt to tip.
RL=ROD LENGTH, RA = ROD ANGLE, H1 = HEIGHT 1, L1 = LENGTH 1
Step 1: We need to make a couple of triangles. Let’s do that by drawing two dotted-lines. One dotted-line will start at the rod butt’s base and extend to the fishing line so it runs parallel to the water. The other dotted-line will start at the rod tip and extend downwards and perpendicular to the first dotted line we created.
We’ll see that we’ve created two smaller right triangles inside of a larger triangle.
Our leftmost triangle contains our rod angle (RA) as well as a 90 degree angle. The rod length (RL) is the hypotenuse of this triangle where length 1 (L1) and height 1 (H1) are variables we need to calculate.
STEP 2: Calculate L1 and H1.
Again we just need to reference that SOHCAHTOA mnemonic. We’ll use the SOH and CAH trigonometric ratios. Rod length (RL) is the hypotenuse (HYP) while height 1 (H1) is the opposite side (OPP) and length 1 (L1) is the adjacent side (ADJ) to the rod angle (RA).
SIN(θ) = OPP/HYP is rewritten into our variables as SIN(θRA) = H1/RL
So multiplying each side by RL gives us: H1 = RL* SIN(θRA)
COS(θ) = ADJ/HYP is rewritten into our variables as COS(θRA) = L1/RL
Multiplying each side by RL gives us: L1 = RL* COS(θRA)
EXAMPLE: Let’s say our fisher here is holding a 6.5’ rod (RL) at an angle of 22.5⁰ (RA).
So H1 = 6.5*SIN(22.5) = 2.487’
and L1 = 6.5*COS(22.5) = 6.005’
STEP 3
Here we will approximate our visible cast (VCL) distance by assigning it a value. As fishers, this length is easier for us to approximate than total cast distance because we can see it.
Visible Cast Length (VCL) – The length between the rod tip and where the line penetrates the water. This is a length parallel to the water (and not running along the fishing line.)
Rod Butt’s Height above Water Level (HAW) – The height between the rod butt and the water level. This distance is measured perpendicular to the water level.
We will also approximate our rod butt’s height above water (HAW) by assigning it a value. Again, this is fairly simple for us to approximate when we are fishing. Typically, a 6” tall angler standing even with the water will be holding that rod butt about 3.5” above the water. On a bass boat platform this will be more like 5.5” and in a kayak it’ll be around 1.5”.
Height of Rod Tip over Water Level (H2) - This height is what we must calculate.
This is simply done by adding H1 (of which we found in Step 2) to HAW. That looks like H2 = H1 + HAW
For our example where our fisher is holding a 6.5’ rod (RL) with a rod angle (RA) of 22.5⁰ the value for H1 is 2.487. So let’s just approximate the HAW to be 3.513 so that we get a nice number.
2.487 + 3.513 = 6.000 = H2
Extra: We didn’t really need to find L1, but it’s sometimes nice to know how far that fishing line penetrating the water is away from the rod butt. Simply just add L1 to VCL to find that distance.
STEP 4
Here we can find our important angle (ΘIA) by examining this right triangle where we know two sides (H2 & VCL) as well as one angle (that 90 degree angle between the sides we know.)
We can still stick with our SOHCAHTOA trigonometric ratios because this is a right triangle. (Using the Law of Cosines will work as well—it just gets more complicated.)
This time we’ll use the TOA or TAN(Θ) = OPP/ADJ trigonometric ratio. For our calculation that looks like: TAN(θIA) = H2/VCL
We’ll want to find θIA so we need to take the inverse tangent of each side. ARCTAN(TAN(ΘIA)) = ARCTAN(H2/VCL) which leaves us with ΘIA = ARCTAN(H2/VCL)
For our example, plugging in the numbers will give us ΘIA = ARCTAN(6/2.5) = 67.38⁰
The important angle is 67.38⁰ in this example.
Now simply just plug that important angle into the PH = SIN(θIA) * TE equation we covered in the quick version of finding play height. (Near the top of this webpage.)
Assuming our fisher tied a 1’ tag end his play height then his play height will be: PH = SIN(67.38) * 1 = 0.923’ which means he didn’t lose much play height from the original tie.
FINDING THE % LOSS OF PLAY HEIGHT
It’s more convenient (at least for me) to understand the rig’s presentation underwater by knowing the percent loss of play height.
If a rig is dropped straight down and the important angle is 90⁰ there won’t be any loss of play height. The entire length of the tag end (the distance between the hook and weight) is playable.
At any other angle, there is a loss of play height on a flat bottom.
We’ve seen how to calculate our play height in the examples above. All we need to know to calculate that percent loss is the play height (PH) and the length of the tag end (TE).
STEP 1: First just divide the play height (PH) by the length of the tag end (TE) and multiply that number by 100. This will give us the percent of the play height (PPH) existing from the original tag end, of which, may be more valuable to you than knowing the percent loss.
PPH = (PH/TE) * 100
STEP 2: Now to get the percent loss of play height (PLPH), simply subtract PPH from 100.
PLPH = 100 – PPH
So for our example, the play height (PH) was 0.923 from a 1’ tag end (TE): PPH = (0.923/1.000)*100 = 92.3%
The percent loss is as follows : PLPH = 100 – 92.3 = 7.7%
That’s a very small percent loss on the drop-shot rig.