Determine Center of Gravity

7/26/2019 Determine Center of Gravity

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Determine Center

of Gravity, and

Roll-Over Angles

on Your VehicleWritten 11!"#

$ran% D&

'a%a Daless#(

Ever thought youwere close to rolling

over? Plug in somenumbers and see!

Included with this extensive documentation is a dynamic spreadsheet that can beused to determine your COG and RollOver angles Please read the documentationbelow to understand how the spreadsheet does it"s #ob $ou can download it )*R*

$eel free to use the +ale Of Contents elo, or sim.ly scroll don

to vie the entire document&

%able o& Contents

/ntroduction

Ca.turing Weights and 0easures

%ools 'eeded
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(easured )alues

Calculated )alues

*EEP +E%,P

O--+C./E (E.+,RE(E'%+

/ength o& 0heelbase /01

0idth o& 0heel %rac2 1ase /%1

-ront .xle 3eight 4 3-5

0EIG3I'G $O,R *EEP

-ront .xle 0eight 0-

Rear .xle 0eight 4 0R5

Rear .xle 0eight (odi&ied 4 0R6

-ront .xle Elevated 4 3-6

Passenger +ide 0eight 4 0P

Calculating the Centers of Gravity

789 %3E 03EE/1.+E CE'%ER O- GR.)I%$ :01CG;

7$9 %3E 03EE/ %R.C< CE'%ER O- GR.)I%$ :0%CG;

7=9 %3E CE'%ER O- GR.)I%$ 3EIG3% :3%CG;

Roll Over Angles

%3E CG 71./.'CI'G POI'%9

.'.%O($ O- . RO// O)ER

C./C,/.%I'G RO// O)ER .'G/E+

+ide Roll Over .ngle 0.R'I'G!!!

>river +ide Roll Over .ngle 7>+RO.9
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Passenger +ide Roll Over .ngle 7P+RO.9

Rearward Roll Over .ngle 7R0RO.9

-orward Roll Over .ngle 7-0RO.9

+,((.R$ O- RO// O)ER .'G/E+

+uning your ee.2s Roll Over Angles

GR.)I%$ +,PPOR% +%R,C%,RE

/engthen the 0heel 1ase or 0iden the 0heel %rac2

0EIG3% %,'I'G

Redistribute Physical 0eight

/ower the Physical /ocation o& 0eight

Remove ,nneeded 0eight

.pply or Remove Cantilevered 0eight

ROA Alarm 3ystem

0I/+O' I'+%R,(E'%+

C of G ROA 3.readsheet

Wor%sheets

(easured )alues

Calculated )alues

Roll Over .ngles

Addendum4 3econd *dition

-ORCE .'> I%+ E--EC%+ O' O,R *EEP+

0hat is a &orce?

>escribing -orce
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0hy all the emphasis on this?

-ORCE >E+CRIP%IO'+
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/ntroduction

+o o&ten in our trail side conversations we tal2 about the CG :Center o& Gravity; o&one *eep being higher or lower than the CG o& another *eep and we relate this notonly to the ability to get up or down a slope but also to the dreaded thought o&rolling over

$et most o& us have never really &igured out where the Center o& Gravity isactually located on our own *eep and similarly what the Rollover .ngles are

0hy haven@t we done this? 0ell to be honest probably because it isn@t so easy todo

%his writeup is an e&&ort to provide a process that most &ol2s can &ollow todetermine with a reasonable degree o& accuracy the Center o& Gravity and

Rollover .ngles &or their own *eep

%here is some mathematics involved here .lgebra Geometry and %rigonometry

3owever i& you are li2e me and not a math wiA 2id don@t let that scare you away I

have automated all the math via an Excel spreadsheet

.ll that is really reBuired is that you &ollow some simple directions ta2e someaccurate weight and distance measurements and then #ust plug the numbers intothe spreadsheet


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I& you hang in here with me and &ollow this process through you will be rewardedwith the locations o& the &ollowing values &or your *eep

%he D>imensional +ingle Point Center o& Gravity o& your *eep as well asthe

0heelbase Center o& Gravity

0heel %rac2 Center o& Gravity

3eight o& the Center o& Gravity

Roll Over .ngles in &our directions

>river +ide

Passenger +ide

-ront

Rear

I& you can use a tape measure get a &ew minutes access to a truc2 7weighing scale9and you can type some numbers into a spreadsheet you can do this


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Ca.turing Weights and 0easures

In this section you will ta2e some speci&ic measurements o& your *eep &ollowingthese three process steps

Preparing your *eep &or o&&road use

(easuring lengths and heights in your driveway

(easuring weights at a truc2 stop scale

+ools 5eeded

$ou will need the &ollowing tools

%ape (easure

.ccess to a truc2 weighing scale &or approximately F minutes

. means to elevate the &ront tires o& your *eep at least 6 inches o&& theground :Ramps bloc2s a trailer with car ramps on it etc;

. 3elper


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0easured Values

>uring this process you will measure and record the values shown in the tablebelow Each will be explained in detail within this document

Please note I have put &ictitious numbers in this table to use in the examplesthroughout this document $ou will need to record your own *eep@s data in thistable &or use in the &ormulas and spreadsheet I have provided a blan2 table atthe end o& this document &or you to use &or this

6ael Value Descri.tion of 0easured Values

6engths

/01 HF in /ength o& the 0heelbase :.xle center to axlecenter;

/%1 F in 0idth o& the %rac2 :Outer tire edge to outertire edge;

)eights

3-5 5J in 3eight o& -ront .xle 3ub :center;&rom the levelground


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3-6 6J in 3eight o& -ront .xle 3ub :center;&rom groundwhile -ront is Elevated

Weights

0- 6KK 0eight on -ront .xle with *eep /evel

0P 65KK 0eight on Passenger side

0R5 66KK 0eight on Rear .xle with *eep /evel

0R6 65F 0eight on Rear .xle when -ront is Elevated

Convert any &ractions to decimal values -or example a wheelbase measurement o&H6 and FL5inchs would be converted to H6D56F inches /01 M H6D56F

3ere is a table to assist you in converting &ractions to decimal &ormat

$ractions to Decimal Conversion Chart

7 $ractions of an /nch 7 Decimal


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5L5 "&"8#9

5LN 6L5 "&1#9"

DL5 "&1:;9

5L 6LN L5 """

FL5 "&!1#9

DLN L5 "&!;9"

JL5 "&

5L6 6L LN NL5 "&9"""

HL5 "&98#9

FLN 5KL5 "&8#9"

55L5 "&8:;9

DL LN 56L5 "&;9""

5DL5 "&:1#9

JLN 5L5 "&:;9"

5FL5 "&=!;9


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Calculated Values

,sing the data values you recorded above the &ollowing values will be calculatedand used in your e&&orts to determine the Center o& Gravity and Rollover angles

6ael Value Descri.tion of Calculated Values

Calculated Values

3-d 6FD in >i&&erence between -ront 3ub Elevated and-ront 3ub when /evel :3-d M 3-63-5;

/01n H5FJin

/ength o& wheelbase when &ront is elevated

:/01nM+R% :/0163-d6;

0Rd 65F lbs 0eight added to rear axle when &ront axle was


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elevated :0Rd M 0R6 4 0R5;

0t NKK %otal 0eight o& your *eep

:0t M 0- Q 0R5;

I& you would li2e you can calculate these values yoursel& I have provided a blan2table &or you to record these values in at the end o& this document 3owever theExcel spreadsheet will per&orm this &or you automagically!

1ee. 3etu.

1e&ore you begin to ma2e any measurements you will need to set your *eep up #ust

as i& you were ready to ta2e it o&& road %his setup vital to accurately determinethe O&&Road Center o& Gravity and Roll Over .ngles o& your *eep

Please do not s2ip this step

0hatever you do to prepare your *eep &or an o&& road trip do the same now

Pac2 that toolbox spare parts 3i/i&t *ac2 and anything else that you wouldnormally bring (a2e sure everything is sa&ely anchored down


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I& you have two sets o& tires one &or the street and another set &or o&& road putthe o&& road tires on and air them down to the level you would use o&& road

-ill your gas tan2

I& you would normally o&& road with someone in the passenger seat or any otherseats &or that matter ma2e sure this &ol2s are available to 2eep these seats warmwhen you are ta2ing the weight measurements

I cannot overemphasiAe the importance o& weight and weight distribution in and onyour *eep to accurately determine the Center o& Gravity $our e&&orts in settingyour *eep up now will be rewarded in accuracy later

Off-3cale 0easurements

%hese measurements should be ta2en away &rom the weight scale so the scale isnot tied up when it isn@t necessary

0ith a &riend measure and record the &ollowing values

6ength of Wheelase- 6W>


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(easure your *eep@s wheelbase length while it is sitting on level ground and &ullyprepared &or an o&& road trip

$our *eep@s wheelbase is the distance between the centers o& the &ront tire&ootprint on the ground and the rear tire &ootprint on the ground %his is a bitdi&&icult to measure accurately however we can get it by measuring the distancebetween the axle hubs

0ith a &riend measure the distance between the center o& the &ront axle hub andthe center o& the rear axle hub %his will be eBual to the length o& your *eep@swheelbase

(a2e all measurements accurate to a 5L5 o& an inch

3ere is a drawing o& what you will need to measure to capture the wheelbaselength


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Remember to convert &ractions to decimal values

Width of Wheel +rac% >ase- 6+>

(easure the distance between the outer edges o& your rear tires %his is the%rac2 0idth o& your *eep Convert any &ractions to decimal values and record thismeasurement in inches as /%1

3ere is a drawing o& the measurement you need to ta2e


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$ront A?le )eight@ )$1

(easure the distance &rom the center o& your &ront hub to the ground and recordthis as 3-5

1e sure your *eep is sitting on level ground when you do this


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Weighing Your 1ee.

>rive your *eep over to the local &riendly neighborhood weigh station

1e sure to bring whatever means you will use to elevate the &ront axle with youand remember to ta2e whatever this is out o& your *eep be&ore you weigh your*eep

.lso remember to put those other warm bodies in their seats be&ore you ta2e anyweight measurement %his includes you too!

otential 3cale 6ocations

(a#or %ruc2 +tops

3ighway Roadside 0eigh +tations

.gricultural Centers :1ul2 Grain +ales;

+alvage $ards

Recycling Centers

%he scale you choose should be accurate to at least F lbs :5 lb would be better;

Once you have identi&ied the scale you would li2e to use I have &ound it help&ul topay a visit to the &riendly scale operator ahead o& time Explain what you want to


19/89

do and how you will do it 1e nice and be &riendly! (aybe even entice the operatorwith a seat in your *eep &or next wee2ends trail ride

I& all else &ails try 5K!

$our ob#ective is to get &ive to ten minutes on that scale!!!

O


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Rear A?le Weight @ WR1

0eigh the rear axle o& your *eep by pulling the &ront tires o&& the scale plate andrecord this weight as 0R5

Rear A?le Weight 0odified @ WR#

$ou must come up with a means to li&t the &ront axle o& your *eep y the tire.atches at least 6inches higher than on level ground

>O 'O% ,+E . *.C< to do this $ou (,+% elevate your &ront axle >Y +)* +/R*A+C)*3or the geometry will be thrown o&& and your calculation will be &lawed%his is truly vital to the success o& this process


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%he &irst time I did this I used a set o& 5Dinch tall car ramps bolted to 56inchsBuare railroad ties $es this was a pain to carry there and bac2 but it allowed meto li&t the &ront by the tire patches a little more than 6 inches

%he second time I did this a &riend volunteered the use o& a &lat bed trailer

0ith the trailer par2ed in &ront o& the scale plate I put the trailer ramps downand my car ramps on top o& the trailer bed I drove my *eep up and managed toget more than DK inches o& li&t above level this way

OY+)* +/R* A+C)*3yet?

Good now weigh the rear axle with the &ront elevated :at least 6 inches; andrecord this weight as 0R6


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$ront A?le *levated @ )$#

(easure the distance &rom the ground to the center o& the elevated &ront hub andrecord this distance as 3-6

assenger 3ide Weight @ W

0eigh the passenger side o& your *eep by pulling only the passenger side tires onthe scale plate Record this weight as 0P


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$ou have now &inished collecting all the data you will need to determine your *eep@sCenter o& Gravity and Rollover .ngles .ll that is le&t is to do is calculate a &ew&ormulas


24/89

Calculating the Centers of Gravity

B +he Wheelase Center of Gravity 'W>CG(

%he easiest Center o& Gravity coordinate to &ind is where the Center o& Gravitylies relative to your *eep@s wheelbase

%he weight on your *eep@s &ront and rear axles is directly proportional to thelocation o& the Center o& Gravity along your *eep@s wheelbase In &act it is a

direct inverse ratio

%hin2 about it

I& 5KKS o& the weight o& your *eep was located on the &ront axle the Center o&Gravity would be located =ERO inches or KS o& the wheelbase distance &rom the

&ront axle

I& the weight were distributed KS on the &ront axle then the Center o& Gravitywould be located KS o& the wheelbase distance &rom the &ront axle

%o calculate your *eep@sW>CG

:0heelbase Center o& Gravity; you will use thedata values you measured and recorded earlier

Once again please remember I am using &ictitious data in these examples $ou willneed to substitute your measurements or type them into the spreadsheet


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6W>M HF inches M 0heelbase in Inches

W$M 6KK lbs M 0eight on -ront .xle

WtM NKK lbs M %otal weight o& *eep

%he &ollowing &ormula will enable you to determine in inches where the W>CGislocated behind your *eep@s &ront axle

'1 - 'W$ Wt(( 7 6W> E W>CGlocation in inches behind the &ront axle

:5 :6KK L NKK;; HF M

:5 KF5J; HF M

K HF M


26/89

BY +he Wheel +rac% Center of Gravity 'W+CG(

%he location o& your *eep@s W+CG:0heel %rac2 Center o& Gravity; is calculated inmuch the same way as you #ust calculated the 01CG

%he 0%CG coordinate location is a direct inverse ratio o& the weight on each sideo& your *eep to the wheel trac2

3ere are the data elements you will need to use &or this &ormula

6+>M F inches 0idth o& your wheel trac2

WM 65KK lbs 4 0eight on passenger side o& your *eep

WtM NKK lbs 4 %otal weight o& your *eep

%he &ollowing &ormula will enable you to determine in inches where the W+CGislocated &rom the outer tire edge on the passenger side o& your *eep

+ubstitute the data values you measured and recorded and then simpli&y and solvethe &ormula as in this example

'1 - 'W Wt(( 7 6+> E W+CGin inches &rom the passenger side tireedge


27/89

:5 :65KK L NKK;; F M

:5 KDJF; F M

KF6F F M !8&98 /nches from the .assenger side outer tire edge


28/89

BF +he Center of Gravity )eight ')+CG(

%he 3eight o& your *eep@s Center o& Gravity :)+CG; is not Buite as easy todetermine

Calculating the 3%CG is a bit more di&&icult to accomplish It@s di&&icult &or somepeople to even visualiAe and di&&icult &or me to explain

/et me give it a shot

0hen you went about measuring and weighing your *eep one o& the things you didwas li&t the &ront axle :at least 6 inches higher than it would be on level ground;and then you weighed the rear axle

0hen you li&ted the &ront you in e&&ect shortened the wheelbase as it relates togravity In other words the horiAontal distance between the &ront and rear tirepatches became shorter than what it is on level ground

3ere is a drawing that might help in understanding this


29/89

'ow i& we can measure how high we li&ted the &ront axle calculate the length o&this shortened wheelbase and determine how much weight was added to the rearaxle when we li&ted the &ront we will be able to calculate the 3eight o& your*eep@s Center o& Gravity :3%CG;

3ere are three &ormulas you must solve be&ore you can get to the 3%CG

)$d E )$# - )$1M 3eight di&&erence between &ront axle level and elevated

3-d M 6J 4 5J


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)$d E#9&! inches

6W>nE3R+ '6W>H# - )$dH#(M /ength o& the shortened wheelbase whenelevated

/01nM+R% :HF6 4 6FD6;

/01nM+R% ::HF HF; 4 :6FD 6FD;;

/01nM+R% :HK6F 4 KKH;

/01nM+R% :NDNH5;

6W>nE=1&9; inches

WRd E WR# @ WR1M 0eight added to rear axle

0Rd M 65F 4 66KK


31/89

WRd E #19 ls&

O 7 6W>n( 'Wt 7 )$d(( MYour ee.2s CG )eight

3%CG M 5J Q ::65F HF H5FJ; L :NKK 6FD;;

3%CG M 5J Q :5NJKD5J6 L 565K;

3%CG M 5J Q 5FK

)+CG E !#&:" /nches aove the tire .atches


32/89

Roll Over Angles

+o where are we?

0e now 2now the 8 $ and = coordinates that de&ine the D> Center o& Gravity o&your *eep

In the example I@ve been using the Center o& Gravity is located at a point

DF Inches behind the &ront axle

DF Inches &rom the passenger side outer tire edge and

D6NK Inches above the *eep@s tire patches

Can you see it?

I& you can &ind the single point represented by these three coordinates you can

&ind the Center o& Gravity o& your *eep!

+ome people can visualiAe thisT others li2e mysel& have a harder time o& it


33/89

-or the sa2e o& this discussion let@s #ust say these three coordinates de&ine theCenter o& Gravity as the Radio )olume Control alancing oint

%he Center o& Gravity represents the single point where the average weight o& the*eep is located $ou can thin2 o& this as the 71alancing Point9

I& you could somehow reach the Center o& Gravity with a long pole you couldsupport the *eep &rom that pole and rotate the *eep in any direction DKdegrees in D> and the *eep would not &all

-ortunately &or us we do not have to support our *eep@s Center o& Gravity &rom apole nor do we want to balance it in a DKdegree sphere 0e do however balance

itT we do this under normal conditions by balancing the Center o& Gravity on ourtire patches


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I& you were to loo2 at the location o& your *eep@s Center o& Gravity &rom the topyou would see that it &alls within the rectangular support structure &ormed by yourtires on the ground

3ere@s a drawing that might help you visualiAe this

%his is goodness! %his is a stable condition!

'otice that the Center o& Gravity is located within the 7Physical Geometry9 o& all&our tires even though it is not centered It is located at the 8 and $ coordinateswhich you calculated

:In all li2elihood your *eep@s Center o& Gravity will not be centered either;


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.nother way to loo2 at this is that the Center o& Gravity :under normal conditions;is being balanced on top o& a pyramid :instead o& a pole; with the Center o& Gravity

at the apex o& &our uneBual sides

%a2e a loo2 at this topview drawing Perhaps it will help you to visualiAe this

.s long as your *eep@s Center o& Gravity is contained within the gravity supportstructure :Gravitational Geometry; &ormed by the tires your *eep will not roll

I& your *eep@s Center o& Gravity is allowed to move outside the gravity supportstructure &ormed by your tires your *eep will roll!


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%his is a basic law o& physics

Anatomy of a Roll Over

I& you position your *eep in such a way that the Center o& Gravity is moved outsidethe gravity support structure o& your tires your *eep will become unstable and willroll

/ets loo2 at this &rom another view &rom the rear

0hen your *eep is on level ground loo2ing &rom the bac2 the Center o& Gravity iscontained between the driver and passenger side tires or in other words withinthe gravitational support structure


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.s your *eep is positioned somewhat o&&camber to the driver@s side the Centero& Gravity :CG; will move closer to the edge o& the gravitational support structure

:green line;

'ote that the Center o& Gravity did 'O% (O)E in relation to the *eep itsel& :Itis still the Radio )olume Control


38/89

0hy do we roll?

0e roll because the Center o& Gravity is no longer balanced under our 7pre&erredgravity support structure9 &ormed by our tires!

%his is a basic law o& Physics

%he Center o& Gravity is always balanced :contained; within the gravitationalgeometry o& some support structure

I& the Center o& Gravity is moved outside one structure :your tires; the Center o&Gravity will be supported by another support structure :/i2e the side o& your*eep!;


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3ere is what this loo2s li2e &or a rearward roll over


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41/89

+imilar drawings &or a passenger side roll over and a &orward direction roll overcould be drawn but I@m tired I@m sure you get it visualiAe these as well

.s you now 2now the Center o& Gravity can be moved outside the gravitationalgeometry o& the support structure &ormed by the tires 0hen this happens the*eep will roll

1ut when will this happen?

%his will happen at a certain angle in each o& &our directions based on the locationo& your *eep@s Center o& Gravity

3ere@s how to calculate these angles &or your *eep

Calculating Roll Over Angles

I& you have done the wor2 to determine where the Center o& Gravity is located &oryour *eep you have all the in&ormation you need to calculate your &our roll overangles

3ere are the data elements you will be using


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ReJuired Data *lements to Determine Roll Over Angles

6ael Value Descri.tion of Data *lement for Roll Over Angles

/01 HF in /ength o& the 0heelbase :.xle center to axle center;

/%1 F in 0idth o& the %rac2 :Outer tire edge to outer tire

edge;

01CG DF 0heel 1ase Center o& Gravity behind -ront .xle M

:5 :0- L 0t;; /01 M 01CG

0%CG DF 0heel %rac2 Center o& Gravity &rom the passengerside outer tire edge M :5 :0P L 0t;; /%1 M 0%CG

3%CG D6NK $our *eep@s CG 3eight M

3-5 Q ::0Rd /01 /01n; L :0t 3-d;; M 3%CG

Please note the &ormulas that &ollow contain the trigonometry &unction o& .rc%angent which presents a solution in 7Radians9 :$es radians are totally useless inthe *eep@n world unless you@re a roc2et scientist;


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Radians are then converted into 7>egrees9 :I understand degrees!; through the useo& a published standard mathematics table

1oth .rc %angents and Radian to >egree Conversions are outside my ability toexplain in this document

%his is the only time I will as2 &or your &aith without an adeBuate explanation'ewton Galileo and Einstein have all proved this &unctions out %hat@s good enough&or me I hope it is good enough &or you as well

$ou can per&orm these calculations on most good scienti&ic calculators or you canuse the Excel spreadsheet I will provide to do this math automagically &or you


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3ide Roll Over Angle - WAR5/5GKKK

.s stated at the top o& this writeup this process will help you determine theCenter o& Gravity and Roll Over .ngles &or your *eep 7with a reasonable degree o&accuracy9

%hat is true however I need to ma2e you aware o& a particular o&&road conditionand it@s potential e&&ects on +ide Roll Over .ngles

%his is important because it is 'O% .>>>RE++E> in these &ormulas

In truth I do not 2now how to calculate these variables

I do 2now it is prudent to ma2e you aware o& any potential that could >ECRE.+Eyour +ide Roll Over .ngles and present you with a rather unpleasant surprise

6*A3* R*AD +)/3K

+he formulas for Driver and assenger 3ide Roll Over Angles DO 5O+ ta%e

into consideration or calculate the .otential effect of the don-slo.e tires

Brolling, sliding or tuc%ing under the heels


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3ow much your tires may 7tuc29 under the wheels will depend on tire siAe pro&ileair pressure sidewall strength and slope o& the angle

0hen tires 7tuc29 under the wheels two physical events occur

5 %he Physical 0idth o& your *eep@s 0heel %rac2 is shortened

%his in combination with the angle your *eep is on will result in an ,'ECRE.+E in Roll Over .ngle! :%his is 'O% Goodness;

6 %he )ertical 3eight o& your *eep@s Center o& Gravity will be lowered

%his will result in an ,'


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Please note I do not 2now o& any means o& calculating these e&&ects at this time

Perhaps in the near &uture we will


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Driver 3ide Roll Over Angle BD3ROA

0hat we will be determining is how many degrees to the le&t you can ta2e your*eep be&ore the Center o& Gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires

3ere is a drawing o& what we are going to solve

%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the outer edge o& the driver

side tire and the Center o& Gravity o& your *eep

%he angle that is &ormed between these two lines is the >river +ide Roll Over.ngle


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3ere is the &ormula we will use to calculate the D3ROA

D3ROA E D*GR**3 'A+A5 ''6+>@W+CG()+CG((

>+RO. M >EGREE+ :.%.' ::F4DF;LD6NK;;

>+RO. M >EGREE+ :.%.' :6NLD6NK;;

>+RO. M >EGREE+ :.%.' :KNJKJD5;;

>+RO. M


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assenger 3ide Roll Over Angle B3ROA

0hat we will be determining is how many degrees to the right you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure o& your tires


%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the outer edge o& thepassenger side tire and the Center o& Gravity o& your *eep


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%he angle that is &ormed between these two lines is the Passenger +ide Roll Over.ngle

.nd here is the &ormula we will use to calculate the 3ROA

3ROA E D*GR**3 'A+A5 'W+CG)+CG((

P+RO. M >EGREE+ :.%.' :DFLD6NK;

P+RO. M >EGREE+ :.%.' :555D5;

P+RO. M


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Rearard Roll Over Angle BRWROA

0hat we will be determining is how many degrees to the rear you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires


%he vertical blue line represents the vertical pull o& gravity on your *eep It

intersects the angled pin2 line which runs between the centerline o& the rear tirepatch and the Center o& Gravity o& your *eep

%he angle that is &ormed between these two lines is the Rearward Roll Over .ngle


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.nd here is the &ormula we will use to calculate the RWROA

RWROA E D*GR**3 'A+A5 ''6W>@W>CG()+CG((

R0RO. M >EGREE+ :.%.' ::HF4DF;LD6NK;;

R0RO. M >EGREE+ :.%.' :F5LD6NK;;

R0RO. M >EGREE+ :.%.' :5FNHK6;;

R0RO. M 9;&ac%ard E Rearard Roll Over Angle

$orard Roll Over Angle B$WROA

0hat we will be determining is how many degrees to the &ront you can ta2e your*eep be&ore the center o& gravity pierces the vertical plan o& gravity and extendsoutside the gravitational support structure &ormed by the tires



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%he vertical blue line represents the vertical pull o& gravity on your *eep Itintersects the angled pin2 line which runs between the centerline o& the &ront tirepatch and the Center o& Gravity o& your *eep

%he angle that is &ormed between these two lines is the -orward Roll Over .ngle

.nd here is the &ormula we will use to calculate the $WROA

$WROA E D*GR**3 'A+A5 'W>CG)+CG((

-0RO. M >EGREE+ :.%.' :DFLD6NK;;

-0RO. M >EGREE+ :.%.' :5D6JDH;;


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-0RO. M 9!&"1 Degrees $orard E $orard Roll Over Angle


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3ummary of Roll Over Angles

%he Roll Over .ngles we #ust calculated &or our &ictional *eep will loo2 li2e this


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+he )igher the Roll Over Angle the >etterK

%hin2 o& the Roll Over .ngle as a bu&&er the de&ined operating range in all &ourdirections where your *eep will remain stable and unli2ely to roll over

%he greater this range :angle; the more you will be able to 7sa&ely conBuer9 in your

*eep

Can you see the relationship between the physical location o& the *eep@s Center o&Gravity and the *eep@s gravitational support structure :tire patches;?

+he greater the horiLontal distance eteen your ee.2s Center of

Gravity and the tire .atch, the greater the Roll Over angle ill e&

Chec2 it out in the drawing above

Can you see the relationship between the 3eight o& the Center o& Gravity and eachRoll Over .ngle?

+he loer you can get your ee.2s Center of Gravity to the ground, the

greater all of your ee.2s Roll Over Angles ill e&


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Conversely i& you raise your *eep@s Center o& Gravity you will decrease all o& your*eep@s Roll Over .ngles


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+uning your ee.2s Roll Over Angles

'ow that you 2now how to calculate the Center o& Gravity and the Roll Over .ngles&or your *eep the Buestion becomes 70hat to do with this in&ormation?9

0ell one thing you can do is 7tune9 your *eep to get the Center o& Gravity and RollOver .ngles more to your li2ing

3ere are a &ew o& the many actions you can ta2e to 7tune9 your *eep@s Center o&Gravity and Roll Over .ngles

/engthen wheelbase andLor wheel trac2

Redistribute Physical 0eight

/ower /ocation o& Physical 0eight

Remove ,nneeded 0eight

.pply or Remove Cantilevered 0eight

Gravity 3u..ort 3tructure

6engthen the Wheel >ase or Widen the Wheel +rac%


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%his action will increase the siAe o& the gravitational support structure on whichthe Center o& Gravity is balanced and increase your *eep@s Roll Over .ngles:Goodness;

/engthening the wheelbase or widening the wheel trac2 is something a2in to puttingoutriggers on a canoe %hey help 2eep it &rom turning over

Weight +uning

%he next &our examples all deal with weight %o best understand these it would behelp&ul to have a general understanding o& the e&&ects o& 7weight placement9 on

your *eep

0here weight is placed along the wheelbase o& your *eep or even outside the

wheelbase o& your *eep will have signi&icant e&&ects on the weight carried by eachaxle %his will a&&ect the location o& the Center o& Gravity and your *eep@s RollOver .ngles

%he closer weight is located to the center o& your *eep@s wheelbase the moreeBually that weight will be distributed on both axles :+ee Green =one in drawingbelow;

.s the weight is moved closer to one o& the axles a higher percentage o& weightwill be placed on that axle and a smaller percentage o& weight will &all over the axle&arthest away :+ee 1lue =ones;


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%hings get real interesting when we hang or cantilever weight beyond your *eep@swheelbase

Cantilevered weight has the most dramatic e&&ect on the weight distribution :+eeRed =ones;

Redistriute hysical Weight

Redistribute physical weight &rom one part o& your *eep to another part

%his will move the Center o& Gravity in the direction you are moving the weight andaway &rom the location where the weight came &rom


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%his will alter Roll Over .ngles :Could be good or not so good;

6oer the hysical 6ocation of Weight

.ny time existing weight can be lowered you will lower the Center o& Gravity o&your *eep

. lower Center o& Gravity will create greater Roll Over .ngles :Goodness;

Remove Mnneeded Weight

Removing unneeded weight will a&&ect the height o& your *eep@s Center o& Gravity

3owever be aware! Removing weight can either raise or lower the height o& your*eeps Center o& Gravity

0eight you remove that was 1E/O0 the original 3eight o& the Center o&Gravity will cause the new Center o& Gravity to rise :%hin2 removing yours2id plates;


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I& the Center o& gravity goes up the Roll Over .ngles will >ecreases :'otgoodness;

0eight that you remove that was .1O)E the originally 3eight o& theCenter o& Gravity will result in a new lower Center o& Gravity :%hin2removing a hard top;

I& the Center o& Gravity goes down the Roll Over .ngles will increase :Goodness!;

A..ly or Remove Cantilevered Weight

$es this is the real interesting weight placement

.ny weight hanging in &ront o& the &ront axle or behind the rear axle is calledcantilevered weight

Cantilevered weight has a 7&orce multiplying9 e&&ect on the weight distributionover your axles and on the location o& your *eep@s Center o& Gravity

%here are two uniBue physical e&&ects o& cantilevered weight


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5 Cantilevered weight will increase the weight on the nearest axle by anamount GRE.%ER than the actual weight being added

6 Cantilevered weight will cause a &ractional >ECRE.+E in the weight on theaxle &arthest away

%he e&&ects o& cantilevered weight on your *eep can be calculated prior to actuallyadding the weight

3ere are the data elements you will need and the &ormulas to calculate the e&&ectso& cantilevered weight

Date *lements ReJuired to Calculate *ffects of Cantilevered Weight

.dd0 0eight o& the ob#ect you are going to place in a cantileveredposition

Cant> %he distance &rom the axle center to the weight you areadding

/01 %he length o& your *eep@s 0heelbase


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In this example we will add a winch and mounting plate to the &ront o& a *eep

AddW E 19" lsM 0eight o& winch and mounting plate

CantD E #8 inchesM >istance to &ront axle center &rom center o& the winchplate

6W> E =9 inchesM /ength o& the *eep@s 0heelbase

3ere is a &ormula that can be used to determine the weight that will be added tothe &ront axle as a result o& mounting a 5FK lbs winch on the &ront bumper

'AddW 7 CantD( 6W> I AddW E Weight added to front a?le

:5FK 6; L HF Q 5FK M

:DHKK L HF; Q 5FK M

5KF Q 5FK M 1=1&"9 ls added to front a?le


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.nd here is the &ormula to determine the how much weight will be removed &romthe rear axle as a result o& mounting this winch on the &ront bumper

'AddW 7 CantD( 6W> E 'Weight removed from Rear A?le(

:5FK 6; L HF M

:DHKK L HF; M


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%he *eep@s 0heelbase Center o& Gravity was also changed It was shi&ted&orward toward the &ront axle by a multiple o& the weight added

I& you care to you can go bac2 and recalculate the new 01CG by adding andsubtracting these weights &rom the &ront bac2 and total o& our example *eep$ou will see that the 0heelbase Center o& Gravity has indeed been moved &orwardas a result o& mounting the winch on the &ront bumper


68/89

ROA Alarm 3ystem

I am in the process o& developing a twoaxis :8 and $; Roll Over .ngle .larm+ystem &or my *eep %his system will monitor the dynamic angles on my *eep andprovide a warning when I am approaching prede&ined Roll Over .ngles

%his e&&ort is currently incomplete

%his RO. .larm +ystem will incorporate the &ollowing design &unctions andattributes

Provide the ability to monitor my *eep@s dynamic angles

Enable the setting o& individual roll over angle 7trigger points9 in degrees in&our directions :/e&t Right -orward 1ac2ward;

Provide an audible alarm when trigger points have been reached

.ll 7trigger points@ will have a built in design error o& 6 to D degrees to

provide a margin o& sa&ety

+ystem must be small :*eep real estate is valuable; and easily mounted andremoved &rom the inside o& my cab


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+ystem must be relatively inexpensive :5KK (ax; and be within thecapabilities o& a reasonably s2illed person to build

Wilson /nstruments

Recently I have become aware o& a patent pending product called ClinoExtremewhich is made by the &ol2s at 0ilson Instruments in +acramento C.

0hile I am still trying to get my hands on one o& these units my &irst and secondglace tells me this may be exactly what I am loo2ing &or I& it is and the cost is

reasonable I will drop my e&&orts to develop my own Roll Over .ngle .larm +ystem

I& you have an interest in learning more about this 0ilson Instruments producthere is their web address

httpLLwwwwilsoninstrumentsm&gcomLclinoextremehtm


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3ere are the highlights o& the ClinoExtreme unit as I understand them

>ual Electronic Clinometers :-rontL1ac2 Pitch and +ide to +ide Roll;

'o moving parts :accept &or the gauge needles;

0arning .ngle .larms programmable by the end user via a R+6D6 computerinter&ace

Cost is un2nown at this time

0hen I get my hands on one o& these units I will let you 2now how it wor2s out &orme


71/89

C of G ROA 3.readsheet

I have a complete Excel spreadsheet titled 7CoGURO.xls9 which will accompanythis writeup

%here are two pages to this spreadsheet titled 7COGRO.9 and 7>ata Collection9

,se the COGRO. page to enter your *eep@s weights and measurement and obtainyour *eep@s Center o& Gravity and Roll Over .ngles

%he 7>ata Collect9 page is optional I am trying to collect data pertaining to thistopic

I am reBuesting that you complete this page and sent the entire spreadsheet to>aless6V$ahoocom

I plan to build an online database that will let you compare your *eep@s CG and RO.to other *eeps in your class

.ll data will be added to the database anonymously
mailto:[email protected]:[email protected]


72/89


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Wor%sheets


75/89

I have a complete Excel spreadsheet titled 7CoGURO.xls9 which will accompanythis writeup

0easured Values

6ael Value Descri.tion of 0easured Values

6engths

/01 in /ength o& the 0heelbase :.xle center to axlecenter;

/%1 in 0idth o& the %rac2 :Outer tire edge to outertire edge;

)eights

3-5 in 3eight o& -ront .xle 3ub :center;&rom the levelground

3-6 in 3eight o& -ront .xle 3ub :center;&rom groundwhile -ront is Elevated

Weights

0- lbs 0eight on -ront .xle with *eep /evel


76/89

0P lbs 0eight on Passenger side

0R5 lbs 0eight on Rear .xle with *eep /evel

0R6 lbs 0eight on Rear .xle when -ront is Elevated

Calculated Values

6ael Value Descri.tion of Calculated Values

Calculated Values

3-d in >i&&erence between -ront 3ub Elevated and-ront 3ub when /evel :3-d M 3-63-5;

/01n in /ength o& wheelbase when &ront is elevated

:/01nM+R% :/0163-d6;

0Rd lbs 0eight added to rear axle when &ront axle waselevated :0Rd M 0R6 4 0R5;


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0t lbs %otal weight o& *eep

Roll Over Angles

6ael Value Descri.tion of Data *lement for Roll Over Angles

/01 in /ength o& the 0heelbase :.xle center to axle center;

/%1 in 0idth o& the %rac2 :Outer tire edge to outer tireedge;

01CG in 0heel 1ase Center o& Gravity behind -ront .xle M

:5 :0- L 0t;; /01 M 01CG

0%CG in 0heel %rac2 Center o& Gravity &rom the passengerside outer tire edge M :5 :0P L 0t;; /%1 M 0%CG

3%CG in $our *eep@s CG 3eight M

3-5 Q ::0Rd /01 /01n; L :0t 3-d;; M 3%CG


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Addendum4 3econd *dition

$orce and its effects on our 1ee.s

%here will be a 7+econd Edition9 o& this writeup that will &ocus more on exploringthe dynamic e&&ects o& &orce on our *eeps roll over angles as they may occur in theo&& road environment

I thought it might be help&ul here to provide a baseline understanding o& the

&orces o& physics so we could begin to give some thought to which &orces mightapply in what circumstances

Please note that I am not a physicist but rather an interested *eep@r #ust li2e you%his is my attempt to ta2e a complex sub#ect and simpli&y so we may betterunderstand the &orces our *eeps are interacting with and against

What is a forceN

Our *eeps are constantly interacting with many &orces in the o&& roadenvironment 1ut what is a &orce?

. &orce is a push or pull on our *eeps as a result o& an interaction with some otherob#ect say your *eep@s &ront tire against a roc2 or your entire *eep against asigni&icant climb


79/89

0henever there is an interaction between your *eep and another ob#ect there is&orce acting on both

0hen the interaction stops :you ma2e it to the top o& that steep hill climb; your*eep is no longer experiencing the &orce o& the climb

In Physics a &orce only exists as a result o& an interaction between two :or more;ob#ects In the *eeping world a &orce exists as a result o& an interaction betweenour *eep and anything else we encounter on the trail

-orce interactions between your #eep and everything you encounter on the trail canbe put in one o& two categories

Contact -orces

.ctionata>istance -orces

Contact $orces

%hese are the types o& interaction &orces that come into play when your *eep is

physically in contact with another ob#ect

Contact -orces include


80/89

-rictional -orce

%ensional -orce

'ormal -orce

.ir Resistance -orces

.pplied -orce

Action-at-a-Distance $orces

-orces o& this type occur when our *eeps interact with another ob#ect while not inphysical contact with it but are still able to exert a push or pull despite thephysical separation

Examples o& .ctionata>istance -orces include

Gravitational -orces

Electrical -orces

(agnetic -orces

Descriing $orce


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-orce is measured using a standard metric unit 2nown as the 'ewton

'ewton :the one who had the apple &all on his head while sitting under a tree;developed a set o& &ormulas that are used to convert any o& these nine de&ined&orces into a common unit o& measurement %hat unit o& measurement is called a'ewton

%his means Gravitational Pull can be expressed in 'ewtons and -rictional -orce can

also be expressed in 'ewtons .s can the rest o& the &ield

>on@t worryT we@re not going to go here I don@t have anything against 'ewtons:3ec2 I eat them with &igs inside Buite o&ten; 1ut 'ewtons aren@t exactly a parto& my every day vocabulary let alone my *eeping experiences

0e will use more normal words li2e Pounds or P+I or -tL/bs (easures that Ireadily understand without having to calculate an incredible &ormula &or 'ewtons&or 5F minutes and &orgetting why I wanted to 2now the in&ormation in the &irstplace!

Vector uantity for $orce

%here is something we must understand that applies to all &orces and that is the7vector Buantity &or &orce9


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-orces acting on your *eep have a vector Buantity having both magnitude :siAe; anddirection

In order to convey how a &orce is acting on your *eep you must be able to describeboth its magnitude :siAe; and its direction and it is best to do this in a drawing

You cannot say 1" 5etons:0e will use anything but 'ewtons; is a &ulldescription o& the &orce acting on your *eep or a part o& your *eep

You can say1" 5etons, donardsand you would be giving a &ull and completedescription o& a &orce +ee what I am getting at?

1oth the magnitude :5K 'ewtons; and the direction :downwards; are described

1ecause &orce is a vector and it has a magnitude :siAe; and a direction we have toagree on a way to represent &orce in &uture drawings I would li2e to suggest thisapproach It is loosely based on standard called 7&reebody diagrams9 commonlyused in Physics

In our vector diagrams we will use the siAe o& the arrow to re&lect themagnitude or siAe o& a &orce even i& we don@t 2now exactly what that siAeis

%he direction o& the arrows will give the direction in which the &orce isacting


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3ere is an example o& what this will loo2 li2e in the second edition

O&ten one &orce on your *eep is canceled out by another &orce acting on your*eep

In the above drawing KKK lbs o& gravitational pull is canceled out by KKK lbs o&

push &rom the tires In this case two &orces 7balance each other9

1ut &orce can also go unbalanced I& we add a third &orce to the above drawing youwill better be able to visualiAe this


84/89

%he same two 71alancing -orces9 are acting on your *eep and canceling each otherout

0hen a third &orce is now applied in this case an unbalanced &riction &orce astate o& &orward motion exists

$our *eep moves &orward because there is no counterbalancing &orce to stop it!

0ant a counterbalancing &orce? .pply your bra2es! :.ny idea what type o& &orceyour bra2es would be applying? $es you@re right! -rictional!;


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Why all the em.hasis on thisN

0ell you don@t have to have a Ph> in Physics but you do have to &ully understandtwo points in order to understand what &orces are acting on your *eep

(ore than one &orce can be acting on your *eep at any moment in time

.ll &orce has two dimensions (agnitude :siAe; and >irection

I& you understand these two points you have all the tools you need to begin to&igure out what is happening with your *eep in many o&& road situations

$orce Descri.tions

3ere is a short explanation o& seven o& the nine &orces which are most li2ely tocome into play in the *eeping world Please note I pulled this right out o& the boo2

A..lied $orce4


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.n applied &orce is a &orce that is applied to an ob#ect by another ob#ect or by aperson

I& a person is pushing a des2 across the room then there is an applied &orce actingupon the des2 %he applied &orce is the &orce exerted on the des2 by the person

Gravitational $orce4

%he &orce o& gravity is the &orce with which the earth moon or other massivebody attracts an ob#ect towards itsel&

1y de&inition this is the weight o& the ob#ect

.ll ob#ects upon earth experience a &orce o& gravity that is directed WdownwardWtowards the center o& the earth %he &orce o& gravity on an ob#ect on earth isalways eBual to the weight o& the ob#ect

5ormal $orce4

%he normal &orce is the support &orce exerted on an ob#ect that is in contact withanother stable ob#ect


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.ir resistance is a special type o& &rictional &orce that acts upon ob#ects as theytravel through the air

/i2e all &rictional &orces the &orce o& air resistance always opposes the motion o&the ob#ect

%his &orce will &reBuently be ignored due to its negligible magnitude It is mostnoticeable &or ob#ects that travel at high speeds :eg a s2ydiver or a downhills2ier; or &or ob#ects with large sur&ace areas

:$ea li2e a *eep the &unctional eBuivalent o& drive a bric2 with a tent on top downthe highway; :Couldn@t help mysel& I had to add that;

+ensional $orces4

%ension is the &orce that is transmitted through a string rope or wire when it ispulled tight by &orces acting at each end

%he tensional &orce is directed along the wire and pulls eBually on the ob#ects oneither end o& the wire

3.ring $orce


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%he spring &orce is the &orce exerted by a compressed or stretched spring uponany ob#ect that is attached to it

%his &orce acts to restores the ob#ect which compresses or stretches a spring toits rest or eBuilibrium position

-or most springs the magnitude o& the &orce is directly proportional to the amounto& stretch or compression

Date post:	01-Mar-2018
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Determine Center of Gravity

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