Why do I need to learn math?

[NM156]

I recently heard conversation by a young model enthusiast who stated "Why do I have to learn math in school, I'll never use it".

Personally I have always found that real world examples tend to validate the learning experience.

If you are a builder, maker etc., you most certainly will use math to various degrees. In fact I would guess that most of you already know that. But here is something that could be used as a STEM demonstration that is a simple and practical, but effective, use of trigonometry.

(To make things easier, we'll just work in degrees and ignore the use of radians).

Example 1 (top)
Example 2 (bottom)

EXAMPLE 1:

How much dihedral does your 36" wing have?

Place the wing on a table with one side resting on the table. A triangle is formed between the table, the lower wing surface and the wingtip height from the table.

The adjacent side is half of the wingspan. 18 inches.
The opposite side is the height of the bottom of the tip to the table. 0.63 inches
To solve we will use the arc tangent (inverse) function.


atan(opposite / adjacent)

atan(0.63 / 18.0)

atan( 0.035 ) = 2.00


The answer is 2.00 degrees of dihedral.


EXAMPLE 2:

You want to have 3 degrees of total dihedral in your wing, how high should the tip be when the wing halves are joined?

Assume a 40 inch wing span. Again we will use the tangent function, since we are still using the opposite and adjacent sides, but this time we have an angle supplied.

tan(dihedral) * (wingspan/2)

tan(3) * 20 = 1.047

The answer is to raise the wingtip 1.047 when joining the halves.


PS
The arctan function is available on the Windows calculator in "Scientific" mode under "Trigonometry" when 2nd is depressed. (tan-1)
Ensure that the mode is in DEG.

PPS
The irony does not escape me that the example drawings were done in CAD and solved the equations!!!

 

[Merv]

I totally agree. Once a person knows why they need to learn something, their attitude completely changes. Now it's nolonger a fight to make them learn, now they want to learn.

Now all you need to do is turn them loose and get out of the way.

 

[Flying Monkey fab]

Yup, I am so disappointed in my math books and teachers of 50 years ago. Most of us could write so much better word problems than the old " a train leaves the station in Chicago..." type. The Navy taught me More algebra and practical Trig and then immediately showed me practical application. I've been using them ever since.

 

[The Fopster]

Life is easier with some maths skills in my opinion. I use it all the time professionally and in my personal life. I think everyone should be taught maths and physics to prepare them for the world, but I know others have a different view. My wife, for one!

 

[Pieliker96]

I recently heard conversation by a young model enthusiast who stated "Why do I have to learn math in school, I'll never use it".

Personally I have always found that real world examples tend to validate the learning experience.

If you are a builder, maker etc., you most certainly will use math to various degrees. In fact I would guess that most of you already know that. But here is something that could be used as a STEM demonstration that is a simple and practical, but effective, use of trigonometry.

(To make things easier, we'll just work in degrees and ignore the use of radians).

Example 1 (top)
Example 2 (bottom)
View attachment 219435

EXAMPLE 1:

How much dihedral does your 36" wing have?

Place the wing on a table with one side resting on the table. A triangle is formed between the table, the lower wing surface and the wingtip height from the table.

The adjacent side is half of the wingspan. 18 inches.
The opposite side is the height of the bottom of the tip to the table. 0.63 inches
To solve we will use the arc tangent (inverse) function.


atan(opposite / adjacent)

atan(0.63 / 18.0)

atan( 0.035 ) = 2.00


The answer is 2.00 degrees of dihedral.


EXAMPLE 2:

You want to have 3 degrees of total dihedral in your wing, how high should the tip be when the wing halves are joined?

Assume a 40 inch wing span. Again we will use the tangent function, since we are still using the opposite and adjacent sides, but this time we have an angle supplied.

tan(dihedral) * (wingspan/2)

tan(3) * 20 = 1.047

The answer is to raise the wingtip 1.047 when joining the halves.


PS
The arctan function is available on the Windows calculator in "Scientific" mode under "Trigonometry" when 2nd is depressed. (tan-1)
Ensure that the mode is in DEG.

PPS
The irony does not escape me that the example drawings were done in CAD and solved the equations!!!

You don't even have to use inverse trig functions! If you're working with small dihedral angles, the wingtip raise is pretty much the same as the arclength of the wingtip as it's raised, which is equal to the angle times the span:

Tip Raise = Dihedral Angle * Span, Dihedral Angle = Tip Raise / Span

of course the angle is in radians so you'll want to multiply by 180°/pi radians to get degrees. Using this method I get 2°*pi/180°*18" = 0.628" and 3°*pi/180°*20" = 1.047".

Basic math is quite useful for stuff like tail volume coefficient calculations, wing loading calculations, and scaling plans. Some of the more complex stuff approaching calculus comes up in finding the location of the mean area chord, though online calculators will do that for you. In any case a good understanding of basic math, some geometry, rules of thumb and intuition will get you quite far in designing and building RC planes.

 

[NM156]

An excellent example of deriving a solution from a different angle! (Pun intended)

 

[mikedkelly]

If you want to build someone else's plane you need glue. If you want to design and fly your dream plane, you need math.

 

[FlamingRCAirplanes]

If you want to build someone else's plane you need glue. If you want to design and fly your dream plane, you need math.

Well said

 

[Piotrsko]

If you want to build someone else's plane you need glue. If you want to design and fly your dream plane, you need math.

You don't actually need math, but it is one heck of a shortcut over the school of hard knocks.(aka crashing your designs over and over until you learn what's correct[ask me how I know])

 

[Bricks]

It always amazes me how many people cannot count out $ change with out help. Something really so simple.

 

[FlamingRCAirplanes]

I recently heard conversation by a young model enthusiast who stated "Why do I have to learn math in school, I'll never use it".

Builds character.

 

[mikedkelly]

How about this problem that I am currently working on as another example:
The following 3D printed model has a printed weight of 500g with the CG at 48% aft of the nose of the 60 cm fuselage. If you place a 60g motor 95% aft in the fuselage, will a 2200 mAh LiPo have enough sliding room in front of the wing to allow for a CG range between 10 and 25 percent of the wing chord without adding additional weight? You would of course need to include all of your servos and other equipment for the estimate. While you could work this out by putting weights on a paint stirrer and balance it on a dowel, I would argue setting up a quick spreadsheet to see if this model is even worth considering would save a lot of time and heartache.

 

[mikedkelly]

You don't actually need math, but it is one heck of a shortcut over the school of hard knocks.(aka crashing your designs over and over until you learn what's correct[ask me how I know])

Agreed. Those hard knocks also lead to experience where eventually you will look at a plane and say "Something doesn't look right. I wouldn't fly that." So there is merit on both sides.

 

[Monte.C]

How about this problem that I am currently working on as another example:
The following 3D printed model has a printed weight of 500g with the CG at 48% aft of the nose of the 60 cm fuselage. If you place a 60g motor 95% aft in the fuselage, will a 2200 mAh LiPo have enough sliding room in front of the wing to allow for a CG range between 10 and 25 percent of the wing chord without adding additional weight? You would of course need to include all of your servos and other equipment for the estimate. While you could work this out by putting weights on a paint stirrer and balance it on a dowel, I would argue setting up a quick spreadsheet to see if this model is even worth considering would save a lot of time and heartache.

View attachment 219717

I couldn't imagine pursuing the design part of this hobby without algebra and some basic geometry. Without a mind that works that way, you should major in Political Science.

 

[Monte.C]

Builds character.

Algebra is the gateway to higher level logical thinking.

But I do understand that not everyone's mind is set up for things like algebra.

 

[Monte.C]

Pursuits where algebra isn't crucial:
Day care coordinator
Activist of any sort
Graphic designer
Political Science professor
Dictator
Pottery instructor or basket weaving instructor

I can't think of any more. I guess that's all of them.

 

[mikedkelly]

At the end of the day, this is a beautiful hobby with endless pursuits in design, construction, technology, and flying skill. I respect the pattern flyers at the field who have years of instinct and muscle memory, and they respect me as a novice who has an autolanding foam core model.

 

[Flying Monkey fab]

Pursuits where algebra isn't crucial:
Day care coordinator
Activist of any sort
Graphic designer
Political Science professor
Dictator
Pottery instructor or basket weaving instructor

I can't think of any more. I guess that's all of them.

There is more maths in being a graphic designer than you realize. Also, at least at the analysis level, some basket weaving gets farther into set theory than you'd think.

 

[Monte.C]

There is more maths in being a graphic designer than you realize. Also, at least at the analysis level, some basket weaving gets farther into set theory than you'd think.

Set theory!
I've actually done this:
Tell a friend that all Maples are deciduous trees, but not all deciduous trees are maples. Some people actually cannot understand the concept. That's ok, those people can take up a career in socio-political activism. Sure you get arrested every now & then but when you do you can feel like a STAR!

(By the way I've worked in major engineering and architectural firms that had dedicated graphic designers - who I respected for sure. They didn't use any higher math.)

Nothing against graphic designers or basket weavers. They're people too.

 

[Quinnyperks]

Converses of conventional statements!