Adapting Office Chair Wheels – Fit 10 Millimeter Diameter Mounting Posts to 9.5 Millimeter or 3/8 Inch Diameter Chair Base Sockets

While attempting to purchase new wheels for an older style office chair, the author discovered that replacement wheels can hardly be found.

As a consequence, modification of a readily available new wheel provided a necessary and good solution for this problem. Such older chairs often require a 3/8 inch or 9.5 millimeter (9.5mm) diameter wheel mounting post.

The following method adapts a new wheel equipped with a 10 millimeter (10mm) diameter post for the purpose. To prevent scratching the finish, wrap the new wheel assembly in a rag and lightly clamp it in a bench vice.

Utilize a 10 x 1 inch bastard (flat) file to remove about 1/2 millimeter (0.5mm) from the post diameter. Remove the retaining "C" clip before filing the post. Use one hand to control the slow rotation of the post while filing it down. About every five minutes, remove the wheel and test the post for fit.

When the post completely slips into the base socket, reinstall the “C” clip and press the new wheel into place. By the author’s experience, four posts can be dressed to proper fit in about an hour.

This procedure is not recommended for the larger 7/16 inch diameter post because the amount of filing would be too labor intensive.


Disclaimer
Use of any wheel modification details herein are not authorized for any commercial purposes. The author assumes no liability for any omission or error herein.

 

Kinetic Energy Factors of Dynamic Atmosphere - 21st Century Meteorology Wind Scale

Rev.2  Jan.2018
Greater public safety should be achieved if storm forecasting emphasis is placed on kinetic energy of wind, instead of speed. From the kinetic energy factors presented herein, a user gains understanding and appreciation for the forces of strong winds.

Kinetic Energy Factors of Wind - Table I
Relative	Wind Speed			Reference Wind Scales
Kinetic Energy	km/hr	mi/hr	knots	Beaufort	Saffir-Simpson	Fujita EF
0.56	75	47	41	Gale 9
0.62	79	49	43	"
0.68	83	51	45	"
0.75	87	54	47	"
0.83	91	56	49	Storm 10
0.91	95	59	51	"
1.0	100	62	54	"
1.1	105	65	57	Storm 11		0
1.2	110	68	59	"		"
1.3	115	72	62	"		"
1.5	121	75	65	Hurcn 12	1	"
1.6	127	79	69	"	"	"
1.8	133	83	72	"	"	"
1.9	140	87	75		"	1
2.1	146	91	79		"	"
2.4	154	95	83		"	"
2.6	161	100	87		2	"
2.9	169	105	91		"	"
3.1	177	110	96		"	"
3.5	186	115	100		3	2
3.8	195	121	105		"	"
4.2	204	127	110		"	"
4.6	214	133	116		4	"
5.1	225	140	121		"	3
5.6	236	147	127		"	"
6.1	247	154	134		"	"
6.7	259	161	140		5	"
7.4	272	169	147		"	4
8.1	285	177	154		"	"
9.0	299	186	162		"	"
9.8	314	195	169		"	"
10.8	329	205	178		"	5
11.9	345	215	186		"	"
13.1	362	225	196		"	"
14.4	380	236	205		"	"
15.9	398	247	215		"	"
17.4	418	260	226		"	"
19.2	438	272	237		"	"
21.1	459	286	248		"	"
23.2	482	299	260		"	"
25.5	505	314	273		"	"
28.1	530	329	286		"	"
30.9	556	345	300		"	"
34.0	583	362	315		"	"
37.4	612	380	330		"	"
41.1	641	399	346		"	"
Kinetic energy of wind increases by 10% over each preceding step.
WF Cade             TinyURL.com/WxPro             Rev.2 ©Jan.2018

 
Theory
Within this article, wind is modeled as a volume of moving atmospheric gases, with each molecule acting as a single projectile.

Kinetic energy is defined from classical physics, as follows;
E =(1/2)[MV²]

Where; E = "kinetic energy of motion", M = "mass of projectile", V = "velocity of projectile"

The exact mass of a strong wind is uncertain. Consequently, it is virtually impossible to calculate its absolute kinetic energy. However the task is made easy to accomplish, by specifying its kinetic energy relative to a standard magnitude.

The author has selected a base reference from the metric system, which is the modern system of measurement. Consequently the wind velocity of 100 km/hr is defined to possess a kinetic energy of one.

To appreciate a kinetic energy 1.0 wind, try the following experiment. As a passenger in an automobile, which is legally traveling at 100 km/hr (62 mi/hr), hold a hand out the window. With your palm facing forward and held fully open, feel and evaluate the force of such a wind. To be more precise, try this on a day when the local area wind is dead calm.

Scale design should clearly indicate changes in kinetic energy, which are associated with changes in wind velocity. For document Rev.2, the author chose to utilize an energy multiplier of 1.1 for each step. Therefore, any kinetic energy step is 10% greater in magnitude, than the preceding step.

Consequently, kinetic energy of the measured wind exhibits a ten-percent compounded growth rate throughout Table-I. Note that previously published versions of this article utilized 20% kinetic energy steps instead. However, the base wind reference velocity and fundamental equations are identical for all versions.

From any initial step, such a scale approximately doubles in energy magnitude, for every seven-step increase. For example;  (1.1)⁷ = 1.95

For the wind to be measured, let “E” represent kinetic energy, “M” represent mass and “V” represent velocity.

Therefore, the measured wind has kinetic energy; E = 1/2[MV²]

For the reference wind, let “e” represent kinetic energy, “m” represent mass and “v” represent velocity.

Therefore, the specified reference wind has kinetic energy; e = 1/2[mv²]

As a pure thought experiment, consider the wind from any storm with velocity V and instantaneously apply the brakes. As a result, the same wind now possesses the reference velocity of 100 km/hr.

Moreover, mass  M = m  because the measured wind is identical to the reference wind in every respect, except for velocity. Due to cancellation of both the mass and constant terms in the equations which follow, it becomes apparent that the kinetic energy of wind can be expressed as a ratio.

Kinetic energy ratios or force factors of wind; K
K = E/e
K = 1/2[MV²] / 1/2[mv²]
K = V²/v²    ; Eq.1

Solve function Eq.1 for velocity; V
K = V²/v²
V² = Kv²
V= v[K^1/2]    ; Term K^1/2 equals square-root of K
V =  (v)√K   ; Eq.2


For all computations herein, wind velocity must be expressed in metric units of km/hr. Wind velocity (speed) conversion factors follow. Moreover, wind velocity v is defined as 100 km/hr.

(km/hr) = (1.852) x (knots)
(km/hr) = (1.609) x (mi/hr)


Evaluate function Eq.1 for kinetic energy factor; K
K = V²/v²
K = V²/(100)²
K = V²/(10,000)    ; Eq.3

Evaluate function Eq.2 for measured wind velocity V;
V =  (v)√K
V =  (100)√K   ; Eq.4


Function Eq.3 is the innovative wind gauge and significant tool for charting or graphing the kinetic energy development of hurricanes and typhoons. Whereby; Meteorologists can compute Cade Kinetic Energy Factors, for any desired wind.

Within Table-I, column one step elements for "K" are employed as independent variables to determine metric wind velocity. Consequently as functions of the associated "K" factors, the solution set for “V" is computed by function Eq.4.

From Beaufort, Saffir-Simpson and Fajita scales, applicable data elements are mapped onto Table-I. However, some elements of the referenced scales may have fallen between calculated kinetic energy steps and thus do not appear. The Beaufort scale is mapped by wind speed in knots; whereas, the Saffir-Simpson and Fijita Operational EF scales are mapped by miles per hour.

If any measured wind is compared to the reference wind, its calculated “K” factor reports the relative energy multiplier. However, the solution set for K has no units and is only a relative scale. As a function of kinetic energy factors, calculated velocities (speeds) of all winds within Table-I are rounded to the nearest integer value.

The kinetic energy of wind increases in direct proportion to the square of its velocity. As an example, consider a hurricane with the wind speed of 100 mi/hr. From Table-I , the associated multiplier or factor is 2.6. By relative measure, such a storm possesses 2.6 times greater kinetic energy than the reference wind.

But when the same storm increases by seven-steps to 140 mi/hr, the kinetic energy factor becomes 5.1.  Due to a square-law relationship, this 40 mi/hr wind speed increase yields about twice the kinetic energy or force.

Ultimately, innovation must be recognized. A truly good idea can overcome academic inertia and contribute to science; thus making the world a better place.

Conclusion
At a single instant in time, the total wind kinetic energy expended upon a structure equals the summation of impact energies, of each gas molecule. Consequently, it is unnecessary to determine the grand total kinetic energy of such storms. Instead, a novel tool is provided herein for gauging the relative kinetic energy of wind.

Although the total mass of a hurricane often increases daily, the mass contained in any very thin vertical sheet of wind gases is relatively constant. Therefore, comparisons made between different storms will yield valid results. If wind velocity is charted daily, any single storm can be trended for such kinetic energy changes.

In classical physics, velocity V is specified by a vector, which exhibits both magnitude and direction. However within this article, atmospheric gas molecules are considered to be moving horizontally along the positive "x" axis, while both "y" and "z" axis components are zero.

Moreover, both the measured and reference winds are considered to be moving parallel in the same direction, which is a reasonable conclusion. Thus within Table-I, the vector term of "velocity" is replaced with "speed" instead.

Alternative Derivation
Cade Kinetic Energy Factors of Wind

E = (1/2)MV² ; kinetic energy from classical physics

Since atmospheric mass M, per unit volume, is specified by density ρ (rho);
E = (1/2)ρV² ; kinetic energy of air

The following general physics formula for wind force (F) applies to large billboards or the surface of a building;
F= EAC = [(1/2)ρV²]AC
F = (1/2)ρACV²

Definitions;
K = Force ratios of wind or force factors
C = Wind drag coefficient of object
ρ = Mass density of air
A = Frontal surface area of object
Fm = Measured wind force*
Fr = Reference wind force*
V = Measured wind velocity; by km/hr units
v = Reference wind velocity; definition 100 km/hr
*    Wind direction perpendicular to plane of object

Solve for K to make force comparison;
K = Fm / Fr
K = [(1/2)ρACV²] / [(1/2)ρACv²]

Equal terms (1/2), ρ, A, and C cancel out;
K = V²/ v²
K = V²/ (100)²
K = V²/(10,000)

Note: Factor K is identical to Cade function Eq.3.

Property Rights
WF Cade, the inventor of Cade Kinetic Energy Factors of Wind, reserves all herein related engineering science technology patents and copyrights; ©2005 ©2012 ©2013 ©2014. Moreover; the inventor revised, rescaled and re-copyrighted said Rev.2 invention documents ©Jan.2018.

For any business or commercial broadcast meteorology purposes, an applicable business license shall be required for transmission of said gauge data over any; radio, television, telephone, satellite, internet, or other mediums.

However, the following exceptions apply;

Any agency of the United States Federal Government, such as the National Oceanic and Atmospheric Administration, Federal Aviation Administration, Air Force, Army, Navy, Marines, and Coast Guard is permanently exempt from any license requirement.

With proper credit, authors of weather science or meteorology textbooks are authorized to publish the gauge design theory herein and the associated tables of kinetic energy factors for wind.

Moreover; with proper credit, the engineering science analysis and weather physics data contained herein may be utilized world-wide by any; official government weather bureau, educational institution, professor, teacher, student, amateur weather forecaster, storm chaser, amateur (ham) radio operator or individual. Such afore named users are encouraged to utilize the gauge design presented herein and provide web links to this page.

Reference Links
Beaufort Wind Storm Scale; National Weather Service
https://www.weather.gov/mfl/beaufort

Saffir-Simpson Hurricane Wind Scale; National Weather Service:
https://www.weather.gov/hgx/tropical_scale

Fujita Extended Tornado Scale; National Oceanic and Atmospheric Administration.
http://www.spc.noaa.gov/efscale/

Great Hurricanes of History; National Oceanic and Atmospheric Administration
Harvey, Irma, Andrew, Wilma, Rita, Katrina, Martinique, Juan, Jeanne, Ivan, Isabel, Ike, Hugo, Gutav, Galveston Tx,, Frances, Floyd, Fifi, Dominican Republic, Charley, Andrew and The Great Hurricane.
http://www.nhc.noaa.gov/outreach/history/

Appendix
Data within Table-II below utilizes the same algebraic functions and 100 km/hr wind base reference as Table-I.  But function Eq.3 serves instead to compute column one elements, by utilizing metric wind velocity as the independent variable in 10 km/hr intervals.

Both work well and consequently, table selection is a matter of intended application and personal preference. However, the seven-step energy doubling rule does not apply to Table-II data.

Kinetic Energy Factors of Wind - Table II
Relative	Wind Speed			Reference Wind Scales
Kinetic Energy	km/hr	mi/hr	knots	Beaufort	Saffir-Simpson	Fujita EF
0.49	70	43	38	Gale 8
0.64	80	50	43	Gale 9
0.81	90	56	49	Storm 10
1.0	100	62	54	"
1.2	110	68	59	Storm 11		0
1.4	120	75	65	Hurcn 12	1	"
1.7	130	81	70		"	"
2.0	140	87	76		"	1
2.3	150	93	81		"	"
2.6	160	99	86		2	"
2.9	170	106	92		"	"
3.2	180	112	97		3	2
3.6	190	118	103		"	"
4.0	200	124	108		"	"
4.4	210	130	113		4	"
4.8	220	137	119		"	3
5.3	230	143	124		"	"
5.8	240	149	130		"	"
6.3	250	155	135		"	"
6.8	260	162	140		5	"
7.3	270	168	146		"	4
7.8	280	174	151		"	"
8.4	290	180	157		"	"
9.0	300	186	162		"	"
9.6	310	193	167		"	"
10.2	320	199	173		"	"
10.9	330	205	178		"	5
11.6	340	211	184		"	"
12.3	350	217	189		"	"
13.0	360	224	194		"	"
13.7	370	230	200		"	"
14.4	380	236	205		"	"
15.2	390	242	211		"	"
16.0	400	249	216		"	"
16.8	410	255	221		"	"
17.6	420	261	227		"	"
18.5	430	267	232		"	"
19.4	440	273	238		"	"
20.3	450	280	243		"	"
21.2	460	286	248		"	"
22.1	470	292	254		"	"
23.0	480	298	259		"	"
24.0	490	304	265		"	"
25.0	500	311	270		"	"
26.0	510	317	275		"	"
27.0	520	323	281		"	"
28.1	530	329	286		"	"
29.2	540	336	292		"	"
30.3	550	342	297		"	"
31.4	560	348	302		"	"
32.5	570	354	308		"	"
33.6	580	360	313		"	"
34.8	590	367	319		"	"
36.0	600	373	324		"	"
37.2	610	379	329		"	"
38.4	620	385	335		"	"
39.7	630	391	340		"	"
41.0	640	398	346		"	"
Data Charted as a Function of Wind Speed in Steps of 10 Km/Hr
WF Cade             TinyURL.com/WxPro             Rev.2 ©Jan.2018