# Stress without tears book and a few questions.

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by addicted2climbing, Apr 9, 2018.

### Help Support HomeBuiltAirplanes Forum by donating:

1. Apr 9, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
Hello All,

I was recommended this book by a fellow HBA member. I am going through it and sadly I am on page 4 with a question. Did not get too far..:lick: I have attached a few screenshots below with a question.

• I need to solve LW going through the offset points in the drawing. First off I think the equation has a typo and thus the answer is wrong but then again I could be wrong. I think the first part of the equation should be Lt x (204-4) and not (200-4) Can someone verify that there is an error here or not and it should be (204-4)?
• On the fuselage diagram, should the elevator be on the 8" offset line and not in line with the thrust line? Or do they really want to figure out the force of Lt 8" below the elevator?
• the other part I can not figure out is where does this part come from? -(1000 x 4) = 0 I cant seem to sort out why its 1000 x 4? Im a bit rusty on my algebra equation manipulation so it could just be me...

So if I use my thinking that the 200-4 is a typo and use 204-4 I get 200lt = 5800 which gives an answer of LT=29 and not 27 as shown in the book... Can someone check this for me?

Been a while since I worked these sort of calculations so as I said it could be all me that is incorrect but I really want to go through this book and learn as much as I can.

Best regards,

Marc

2. Apr 9, 2018

### plncraze

#### Well-Known MemberHBA Supporter

Joined:
May 12, 2006
Messages:
1,525
313
The problem is worked in the next chapter but there are typos. It forces the reader to work all the problems. It is frustrating

3. Apr 9, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
I actually want to work out all the problems, but as I mentioned above I think there are errors. Can you have a look at what I wrote above and maybe answer my questions. This equation is from part 2 page 4.

Thank you,

Marc

4. Apr 9, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
Ok I have confirmed that 200-4 is a typo and it should be 204-4 and when I do that I get 27 as the answer. However I still dont understand where the 1000 x 4 comes from in the equation? Can someone shed light on this. Please look at the jpegs I included in the original post for the orriginal equation...

t(204−4)−100(6+8)−(1000)(4)=0
Step 1: Simplify both sides of the equation.
t(204−4)−100(6+8)−(1000)(4)=0
200t+−1400+−4000=0
(200t)+(−1400+−4000)=0(Combine Like Terms)
200t+−5400=0
200t−5400=0
Step 2: Add 5400 to both sides.
200t−5400+5400=0+5400
200t=5400
Step 3: Divide both sides by 200.
200t
200
=
5400
200
t=27

Marc

5. Apr 10, 2018

### Chris In Marshfield

#### Well-Known MemberHBA Supporter

Joined:
Jan 29, 2008
Messages:
1,203
995
Location:
Germantown, WI USA
Is it a weight x moment arm thing? 1000 lbs x 4 inches?

6. Apr 10, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
I think that is exactly what it is, just trying to understand why. I am looking back at part one in the book to see why...

Marc

7. Apr 10, 2018

### TFF

#### Well-Known Member

Joined:
Apr 28, 2010
Messages:
11,421
3,167
Location:
Memphis, TN
Just guessing as I don't have the book. Is the X4 not the arm of the neutral point?

8. Apr 10, 2018

### wsimpso1

#### Well-Known Member

Joined:
Oct 19, 2003
Messages:
5,717
2,952
Location:
Saline Michigan
Concept time. Sum of vertical forces is zero. Sum of horizontal forces is zero. Sum of moments is zero. Conventions. Up and forward are positive, moments that would raise the nose are positive.

Taking them in turn:

Sum of vertical forces is zero - Airplane weight is negative, tail down force is negative, lift from the wing is positive and has to be equal in magnitude to weight plus tail down force, but of opposite sense, so W-Lt-Lw = 0 and remember you are subtracting Lt, which is a negative number;

Sum of horizontal forces is zero - You have drag and thrust in opposite directions and same magnitude;

Sum of moments is zero - You can sum moments about any spot you wish. A moment is a force times a length perpendicular to the direction of the force. It seems the author is summing about the center of lift from the wing. All of the forces are dimensioned from the center of wing lift. To answer why 1000*4 - 1000 pounds is the weight and it is vertical, 4" is the horizontal length from CG to center of wing lift. Remember nose up is positive. You have five forces, and so five moments:

Lw*lw = Lw*0" = 0
W*l = 1000Lb*4" = 4000 in-lb nose down
Drag*l = 100 lb*8 = 800 in-lb nose down
Thrust*l = 100*6" = 600 in-lb nose down
Lt*l = Lt*200" = 200*Lt and it is nose up if Lt is down...

So, 0 = -4000 - 800 - 600 + 200 Lt = -5400+200 Lt

solving for Lt: 5400 = 200*Lt, so 5400/200 = Lt = 27lbs down.

Going back to the vertical forces, W-Lt-Lw = 0, 1000-(-27)-Lw = 0, or 1027 = Lw.

If the book does not agree with this, it does appear that you caught a type.

I hope that this helps.

Billski

9. Apr 10, 2018

### PiperCruisin

#### Well-Known Member

Joined:
Jan 18, 2017
Messages:
109
38
Location:
Idaho
I concur. Nice of you to make such a nice post Mr. Billski.

10. Apr 10, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
Hello Billski,

Thank you so much for your concise and informative reply. This was a perfect explanation. I know this book will not be all that useful for serious structural analysis, but what I hope it gives me is enough foundation of understanding that when I open Raymers book or the myriad of other books I bought on this subject enough of an understanding to to try and read the higher level texts. I cant remember who recommended this book to me on HBA but very glad they did.

Take care,

Marc

11. Apr 10, 2018

### nerobro

#### Well-Known Member

Joined:
Nov 6, 2011
Messages:
1,109
312
Location:
Northern Illinois
That's one of my favorite books.

12. Apr 11, 2018

### wsimpso1

#### Well-Known Member

Joined:
Oct 19, 2003
Messages:
5,717
2,952
Location:
Saline Michigan
Thanks for the compliments guys.

I understand how much trouble some folks have getting this topic right in their heads. Once this one makes sense, and we have established the overall method for doing this sort of thing, and the more involved stuff that follows becomes more straightforward. That is the hope, anyway.

This simple analysis was presented in the book to teach method. It was far from complete. Wings make pitching moments, and that was skipped entirely, but once the method is understood, it can be added in quite easily, as can additional moments from landing gear drag, propeller q factor, tailplanes, and so on.

I like Excel for this sort of thing, including getting all of the pieces laid out so you can look at and check each one. It also grows nicely for adding elements.

The hardest part is not in doing analysis, it is in doing analysis that gives you answers that make sense and are worthy of design and build effort...

Billski

13. Apr 11, 2018

### Vision_2012

#### Well-Known Member

Joined:
Apr 21, 2010
Messages:
274
122
Location:
Sometimes when one is studying one source in detail and one becomes frustrated or is simply unsure of results, I find it helpful to find another source. The internet is great for this. I google the subject with the word "tutorial" as this usually results with a website that breaks down the subject matter into steps I can follow. Yootube is great also and is easily searched by subjects.

14. Apr 11, 2018

### Chris In Marshfield

#### Well-Known MemberHBA Supporter

Joined:
Jan 29, 2008
Messages:
1,203
995
Location:
Germantown, WI USA
Ain't that the truth. Ran into this grand collection yesterday when I was trying to grok Euler's buckling:

https://www.engineer4free.com/mechanics-of-materials.html

Back to your regularly scheduled program.

nerobro likes this.
15. Apr 11, 2018

#### Well-Known Member

Joined:
Jan 27, 2012
Messages:
929
258
Location:
Glendale, CA
Hello Billski,

Thanks again for the reply. In the book he mentions all the missing bits and it looks like he will slowly add in more concepts as I progress through it. I am actually a bit stumped on a few things in part 3 but will spend a bit more time with it before I ask a question. Its great to know there are people on here who are willing to lend a hand and explain a bit of this stuff more concisely. I wish I could take a proper college course on this, but sadly nothing near me that works without enrolling in a full university.

Thanks again,

Marc

16. Apr 11, 2018

Joined:
Oct 19, 2003
Messages:
5,717