The Whizz Wheel Mystery.....
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The Whizz Wheel Mystery.....
Okay, so I have a CRP 5 and have read the book, played the DVD ROM, understand that it is a type of slide rule and know, sort of, how to use it.
But here's the mystery. Everything jumps from explaining how to do simple numerical calculations to giving an example of determining drift with no real explanation as to the stage involved.. The problem with the later is that I know how to do it and how to get the answers but don't really understand how or why it works.
Greg
But here's the mystery. Everything jumps from explaining how to do simple numerical calculations to giving an example of determining drift with no real explanation as to the stage involved.. The problem with the later is that I know how to do it and how to get the answers but don't really understand how or why it works.
Greg
Treat the calculation as a triangle of velocities problem. Draw it out very approximately using pencil and paper. Then use a protractor and ruler to do it accurately. Finaly, reproduce the calculation but using the whizzwheel. There - that was easier, wasn't it.
For every calculation before you take the paper (and ideally again while you are using it for real) repeat the initial rough paper geometry. That reinforces the logic behind the application.
For every calculation before you take the paper (and ideally again while you are using it for real) repeat the initial rough paper geometry. That reinforces the logic behind the application.
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The wind side of the slide rule is a clever geometric device for calculating the triangle of velocities. You could do this using trigonometry but, as with almost any mathematical problem, there is a geometric way of doing it, and the wind side of the slide rule does that.
The other side of the slide rule is a traditional slide rule, which is a multiply/divide device. You can google for explanations but in short it works on the principle that to multiply two numbers you take their logarithms, add the logs, and then antilog that to the get the product of the two original numbers. Similarly, to divide A/B you take the log of A, subtract the log of B, and antilog the result to get A/B. In the early 20th century, when calculators did not really exist in any form, engineers used log tables (computed to say 6 significant digits) to do multiplication/division of long numbers. The slide rule implements this again geometrically, using the two scales which you line up, but the result is delivered only to the precision with which you can do this visually; usually one can get to 2 or 3 significant digits. The decimal point you have to position yourself afterwards (mentally); doing 213/74 is the same operation as 2.13/0.0074 on the slide rule. The CRP slide rule carries marks for common conversions e.g. litres to gallons but this is incidental; in no way is this device related to aviation.
The multiply/divide side is useless these days because a £1 calculator does a far better job.
The other side of the slide rule is a traditional slide rule, which is a multiply/divide device. You can google for explanations but in short it works on the principle that to multiply two numbers you take their logarithms, add the logs, and then antilog that to the get the product of the two original numbers. Similarly, to divide A/B you take the log of A, subtract the log of B, and antilog the result to get A/B. In the early 20th century, when calculators did not really exist in any form, engineers used log tables (computed to say 6 significant digits) to do multiplication/division of long numbers. The slide rule implements this again geometrically, using the two scales which you line up, but the result is delivered only to the precision with which you can do this visually; usually one can get to 2 or 3 significant digits. The decimal point you have to position yourself afterwards (mentally); doing 213/74 is the same operation as 2.13/0.0074 on the slide rule. The CRP slide rule carries marks for common conversions e.g. litres to gallons but this is incidental; in no way is this device related to aviation.
The multiply/divide side is useless these days because a £1 calculator does a far better job.
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IO's explanation is certainly effective and succinct. I'd have to say that other than my recent redo of ground school, I have not used a whizz wheel in the last few decades of flying, oping instead for a combination of mental math, and cheap calculators.
Like many things in aviation, whizz wheels seem to have some kind of special aviation cult value, and thus will probably never go away. Their mere presence conveys that a very complex aviation calculation is nearby to need it, and an aviation god close by to use it.
When, finally, they are no longer required in the cockpit, you'll still see them on the bezel of pilot's watches, to be there just in case a math problem must be solved in the absence of all other computing means (including mental), and the user has excellent near vision. That's one reason that many of us older pilots would rather just do it mentally! If the third decimal of the fuel calculation is going to make a difference, you're already in trouble....
Like many things in aviation, whizz wheels seem to have some kind of special aviation cult value, and thus will probably never go away. Their mere presence conveys that a very complex aviation calculation is nearby to need it, and an aviation god close by to use it.
When, finally, they are no longer required in the cockpit, you'll still see them on the bezel of pilot's watches, to be there just in case a math problem must be solved in the absence of all other computing means (including mental), and the user has excellent near vision. That's one reason that many of us older pilots would rather just do it mentally! If the third decimal of the fuel calculation is going to make a difference, you're already in trouble....
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Let me suggest a method that might help you to understand why it works.
Let’s suppose we have
40 knots wind blowing from 180.
100 knots TAS
We want a true track of 210.
Start as usual aligning the wind direction 180 with the True Heading Pointer.
Now instead of just drawing a cross at 40 knots, draw a straight-line arrow down from the centre dot to 40 knots. This arrow represents the wind speed and direction.
Now rotate the window to align the heading 210 with the desired true track of 210 and set the centre dot on 100 knots TAS
Draw a straight-line arrow upwards from the bottom of the airspeed scale (at the top edge of the square wind section) to the centre dot. This arrow represents the speed and direction of flight if there were no wind.
The flight path over the ground will be the resultant of these two arrows. To find this, draw a dotted arrow from the tail of the TAS arrow to the head of the wind speed arrow.
We wanted to fly a track of 210, but this dotted arrow shows that we are actually drifting in a direction that is about 16 degrees to the right of 210.
We obviously need to steer to the left of 210 to eliminate this right drift, but by how much?
We will find out by a process of repeated trial and error with each attempt reducing the error.
We need a situation in which the number of degrees that we are steering to the left of 210 is equal and opposite to the number of degrees that we are drifting to the right. If we achieve this we will track 210.
As a first stab at it we assume that we will steer 16 degrees to the left of 210. To do this we rotate the window so that 210 is 16 degrees to the right of the true Heading pointer. This gives us a heading of 194 degrees.
The end of the dotted arrow now shows our new track. But the drift has reduced to about 9.5 right. Adding this 9.5 degrees to our heading of 194 gives a track of 203.5. This is to the left of our desired track so we have adjusted our heading too far to the left.
As a second stab we rotate the window to align our desired track 210 with 9.5 degrees right drift. We now have a heading of 200.5 and about 11 degrees right drift. Adding 11 to 200.5 gives a track of 211.5. We have now adjusted our heading too far to the right.
As a third stab set 210 against 11 right drift. We now have heading 199
With 11 degrees drift. 199 is 11 degrees to the left of our desired track of 210 and we have 11 degrees right drift.
The left heading adjustment is now equal and opposite to the right drift so we will flow along the desired track.
So what have we done overall?
By inputting the wind and TAS we drew the triangle of velocities. This showed that we were drifting to the right of the desired track.
We then used repeated trial and error to find out how must we need to steer to the left of track to eliminate the drift.
Let’s suppose we have
40 knots wind blowing from 180.
100 knots TAS
We want a true track of 210.
Start as usual aligning the wind direction 180 with the True Heading Pointer.
Now instead of just drawing a cross at 40 knots, draw a straight-line arrow down from the centre dot to 40 knots. This arrow represents the wind speed and direction.
Now rotate the window to align the heading 210 with the desired true track of 210 and set the centre dot on 100 knots TAS
Draw a straight-line arrow upwards from the bottom of the airspeed scale (at the top edge of the square wind section) to the centre dot. This arrow represents the speed and direction of flight if there were no wind.
The flight path over the ground will be the resultant of these two arrows. To find this, draw a dotted arrow from the tail of the TAS arrow to the head of the wind speed arrow.
We wanted to fly a track of 210, but this dotted arrow shows that we are actually drifting in a direction that is about 16 degrees to the right of 210.
We obviously need to steer to the left of 210 to eliminate this right drift, but by how much?
We will find out by a process of repeated trial and error with each attempt reducing the error.
We need a situation in which the number of degrees that we are steering to the left of 210 is equal and opposite to the number of degrees that we are drifting to the right. If we achieve this we will track 210.
As a first stab at it we assume that we will steer 16 degrees to the left of 210. To do this we rotate the window so that 210 is 16 degrees to the right of the true Heading pointer. This gives us a heading of 194 degrees.
The end of the dotted arrow now shows our new track. But the drift has reduced to about 9.5 right. Adding this 9.5 degrees to our heading of 194 gives a track of 203.5. This is to the left of our desired track so we have adjusted our heading too far to the left.
As a second stab we rotate the window to align our desired track 210 with 9.5 degrees right drift. We now have a heading of 200.5 and about 11 degrees right drift. Adding 11 to 200.5 gives a track of 211.5. We have now adjusted our heading too far to the right.
As a third stab set 210 against 11 right drift. We now have heading 199
With 11 degrees drift. 199 is 11 degrees to the left of our desired track of 210 and we have 11 degrees right drift.
The left heading adjustment is now equal and opposite to the right drift so we will flow along the desired track.
So what have we done overall?
By inputting the wind and TAS we drew the triangle of velocities. This showed that we were drifting to the right of the desired track.
We then used repeated trial and error to find out how must we need to steer to the left of track to eliminate the drift.
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I agree with all the prior comments.
When you say:
Is it the actual triangle of velocities that is the issue?
Assuming you have already solved the standard known-TAS known-Track problem (you say you know how):
The wind side is like a stylised map with the departure airfield at the centre of the circles, and the chinagraph dot is where you are after an hour. By definition this is your track.
You fly up the vertical True Heading axis for an hour, the distance travelled is where the small central circle is. In no-wind that is where you are on the map.
What has the wind done to you during the hour? It has moved you towards the chinagraph dot.
So what you should 'see' is a map with where you are (the dot) and where you would have flown to in no-wind (the little circle).
Hope that helps!
When you say:
It's the clever bit that is missing.
Assuming you have already solved the standard known-TAS known-Track problem (you say you know how):
The wind side is like a stylised map with the departure airfield at the centre of the circles, and the chinagraph dot is where you are after an hour. By definition this is your track.
You fly up the vertical True Heading axis for an hour, the distance travelled is where the small central circle is. In no-wind that is where you are on the map.
What has the wind done to you during the hour? It has moved you towards the chinagraph dot.
So what you should 'see' is a map with where you are (the dot) and where you would have flown to in no-wind (the little circle).
Hope that helps!
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It is a pity that iteration is needed in this case, because a trig solution can be done directly, without iteration. But this is geometry... 
What the old RAF navigators don't tell you is that the winds aloft forecast is usually so much in error that the precision possible with the slide rule (or any other exact calculation method) is wasted.
A simple rule of thumb is as good.
At higher speeds, accuracy is less important because the wind effect on the plane is smaller.
Also, it is damn hard to fly a heading to within a few degrees, by hand, for long periods.
And the final nail in the coffin of precise wind calcs is that if you plan reasonably short inter-waypoint distances, say less than 20nm, it is hard to get lost anyway - provided you have chosen clean and unambiguously identifiable ground features. When some early pioneer flew from the USA to the UK, he had to only fly a heading within 10 degrees to hit Ireland, and after that it was a piece of cake. Even the crudest sextant will give you latitude good enough for that. And if you have chosen ambiguous features then you will get lost no matter how accurately you fly, because the visual waypoint identification will naturally take precedence over the calculated heading
GPS has made all this largely redundant.
Mrs DFC will be around in a minute to set us amateurs straight, I am sure
What the old RAF navigators don't tell you is that the winds aloft forecast is usually so much in error that the precision possible with the slide rule (or any other exact calculation method) is wasted.
A simple rule of thumb is as good.
At higher speeds, accuracy is less important because the wind effect on the plane is smaller.
Also, it is damn hard to fly a heading to within a few degrees, by hand, for long periods.
And the final nail in the coffin of precise wind calcs is that if you plan reasonably short inter-waypoint distances, say less than 20nm, it is hard to get lost anyway - provided you have chosen clean and unambiguously identifiable ground features. When some early pioneer flew from the USA to the UK, he had to only fly a heading within 10 degrees to hit Ireland, and after that it was a piece of cake. Even the crudest sextant will give you latitude good enough for that. And if you have chosen ambiguous features then you will get lost no matter how accurately you fly, because the visual waypoint identification will naturally take precedence over the calculated heading
GPS has made all this largely redundant.
Mrs DFC will be around in a minute to set us amateurs straight, I am sure
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When some early pioneer flew from the USA to the UK, he had to only fly a heading within 10 degrees to hit Ireland, and after that it was a piece of cake.
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IO540, before I start, I'm not even a distant relative of DFC.
I take a slight issue with your comments about errors - accuracy of flying a heading, simple rules of thumb (which generate an error) and wind forecasts. The point I try to make when teaching student pilots is that there are a number of factors that all generate errors. It is the pilots responsibility to reduce/remove these errors wherever possible such that the errors he has no control over (notably forecast wind in this scenario) can be isolated and therefore addressed.
I agree, that in the age of GPS etc this stuff is becoming less relevant. However, it is important to instil a mindset whereby pilots analyse their own performance and strive to maintain a high standard. Alternatively, we have pilots who will rely more and more on the Magenta with little/no thought as to how things work.
PS. How does one do pre-flight fuel planning on a GPS - rule of thumb?
I take a slight issue with your comments about errors - accuracy of flying a heading, simple rules of thumb (which generate an error) and wind forecasts. The point I try to make when teaching student pilots is that there are a number of factors that all generate errors. It is the pilots responsibility to reduce/remove these errors wherever possible such that the errors he has no control over (notably forecast wind in this scenario) can be isolated and therefore addressed.
I agree, that in the age of GPS etc this stuff is becoming less relevant. However, it is important to instil a mindset whereby pilots analyse their own performance and strive to maintain a high standard. Alternatively, we have pilots who will rely more and more on the Magenta with little/no thought as to how things work.
PS. How does one do pre-flight fuel planning on a GPS - rule of thumb?
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It is a pity that iteration is needed in this case, because a trig solution can be done directly, without iteration.
One of the reasons that people cannot understand what is happening is the fact that the instruction sheets say things like "rotate the window to align the heading with 11 degrees right drift. It would be better if they were to say " adjust the heading 11 degrees to the left to counteract the 11 degree right drift, then look at the position of the cross to see how this adjustment has affected the drift."
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Though in 1928 Stultz, Gordon and Earhart still managed to hit Wales instead of Ireland IIRC!
It is the pilots responsibility to reduce/remove these errors wherever possible such that the errors he has no control over (notably forecast wind in this scenario) can be isolated and therefore addressed.
How does one do pre-flight fuel planning on a GPS - rule of thumb?
I have a 1300nm range (dry). On nontrivial flights (say anything over 700nm) what I do is look at the distance, assume 140kt TAS (a nice economical speed), look at the winds aloft forecast, if there is a tailwind I ignore it, if there is a headwind I take the biggest likely figure, express that as a % of the TAS, add that onto the ETE (so e.g. a 14kt HW would add 10% to the ETE), and if the result gives me > 2 hours at the destination, then I go (modified somewhat if going to say Greece where the alternates with avgas are sparse). I find that simple procedure is at least as accurate as the wind forecast.
I must admit that without a GPS-connected flow totaliser (whose accuracy is checked on every pump fillup) I would be a lot more conservative. But that is not the same as placing a greater trust in the winds aloft forecast.
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Sorry for the delay, I was on an 11.4 hour trip to Tesco.
Departure was from Trepassey Newfoundland according to Wikipedia.
A much better source is 'Amelia Earhart - The Sound of Wings' but I don't have it in front of me right now. I think Ireland was overcast so they never saw it.
And if you think that was a close call with the fuel, google 'Howland Island'. By today's standards, the accident occurred before they took off.
Where was the departure? That seems an odd mistake to make. A bit dangerous too, given the extra fuel used.
A much better source is 'Amelia Earhart - The Sound of Wings' but I don't have it in front of me right now. I think Ireland was overcast so they never saw it.
And if you think that was a close call with the fuel, google 'Howland Island'. By today's standards, the accident occurred before they took off.
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"Sorry for the delay, I was on an 11.4 hour trip to Tesco."
Sorry to hear that, your Tesco obviously has till queues the same length as my local store, which is why I now shop at Asda.
Perhaps it's just because I'm still a low hours PPL, but I do use the whiz wheel in my flight planning. However I recall spending many stressful hours learning 103 different calculations I could do with the thing...and now use approximately two and a half every time I fly (and suspect I have already forgotten most of the remaining 100.5). Seems I'm not the only one who either does mental calculations or uses a cheap Casio...
Sorry to hear that, your Tesco obviously has till queues the same length as my local store, which is why I now shop at Asda.
Perhaps it's just because I'm still a low hours PPL, but I do use the whiz wheel in my flight planning. However I recall spending many stressful hours learning 103 different calculations I could do with the thing...and now use approximately two and a half every time I fly (and suspect I have already forgotten most of the remaining 100.5). Seems I'm not the only one who either does mental calculations or uses a cheap Casio...
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As an aside, you can get even better accuracy for time/speed/distance/fuel calculations from a cylindrical slide rule (imagine it as a straight slide rule wrapped around a cylinder with another hollow cylinder which slides round it). I have my father's - used in the Oxford chemistry lab in the 1950s - which is good to 4 significant figures.
Needless to say he (like I) uses an electronic calculator these days..!
Tim
Needless to say he (like I) uses an electronic calculator these days..!
Tim
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I used to have a very long British Thornton slide rule, in the early 1970s at school. And a little one in the late 1960s. If you got a really smooth running one (the BT one wasn't) you could get 3 sig digits anytime.
But nobody used them for real by 1973, when the first compact calculators came out, initially at silly prices like £200.
By 1975 one had fully programmable scientific calculators for £50 and would have done the wind triangle with those.
Only in aviation could the slide rule have survived another 45 years
But nobody used them for real by 1973, when the first compact calculators came out, initially at silly prices like £200.
By 1975 one had fully programmable scientific calculators for £50 and would have done the wind triangle with those.
Only in aviation could the slide rule have survived another 45 years
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"One of the reasons that people cannot understand what is happening is the fact that the instruction sheets say things like "rotate the window to align the heading with 11 degrees right drift. It would be better if they were to say " adjust the heading 11 degrees to the left to counteract the 11 degree right drift, then look at the position of the cross to see how this adjustment has affected the drift."
Bang on KW and thank you for your previous entry.
Thank you to all the other loyal subscribers. I have just got in from work so I will have a good play with my Whizz Wheel tomorrow. How exciting.
Out of interest, I was speaking to an army helicopter pilot today. He loves the Whizz Wheel and says he uses it wherever he goes. Apparently, it is great for currency conversions too and he can work it more quickly than a calculator.
Oh me oh my, I think I've got some work to do!!!!!!!!!!!!!
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I have to say I'm not surprised that no one uses a whizz-wheel if they are taught the insanely complex method described by Keith Williams. I can't say that he's wrong, but what a stupendously labour intensive way to do a simple drift calc!
Here are his figures;
40 knots wind blowing from 180.
100 knots TAS
We want a true track of 210.
1) Set wind vector
Set 180 at top of wheel.
Mark a point at 40kts below the centre dot.
2) Set TRK
Set 210 at top.
Using the squared section of the slide draw a vertical line through your wind vector dot. (up/down the scale)
3) Calculate result
Run the slide up to centre over your TAS on the radially expanding section.
Rotate wheel until that previously vertical line is aligned parallel with the radial one/s beneath it.
Read HDG off top of wheel; drift angle, as if you wanted to know it, above the TRK (210) and GS under the wind vector dot.
End.
Isn't that about a tenth the effort of all that to-ing and fro-ing of fudging your guesses until they shape up?
All we are doing is drawing the important part of the vector triangle against a background scale.
What's more I bet most people could do this, and time and fuel calcs on multi legs quicker and more consistently accurately (ie less gross errors) on a whizz wheel than they can on any calculator.
Plus, my Mk4B doesn't quit when the batteries go flat
Here are his figures;
40 knots wind blowing from 180.
100 knots TAS
We want a true track of 210.
1) Set wind vector
Set 180 at top of wheel.
Mark a point at 40kts below the centre dot.
2) Set TRK
Set 210 at top.
Using the squared section of the slide draw a vertical line through your wind vector dot. (up/down the scale)
3) Calculate result
Run the slide up to centre over your TAS on the radially expanding section.
Rotate wheel until that previously vertical line is aligned parallel with the radial one/s beneath it.
Read HDG off top of wheel; drift angle, as if you wanted to know it, above the TRK (210) and GS under the wind vector dot.
End.
Isn't that about a tenth the effort of all that to-ing and fro-ing of fudging your guesses until they shape up?
All we are doing is drawing the important part of the vector triangle against a background scale.
What's more I bet most people could do this, and time and fuel calcs on multi legs quicker and more consistently accurately (ie less gross errors) on a whizz wheel than they can on any calculator.
Plus, my Mk4B doesn't quit when the batteries go flat