US3168389A

US3168389A - Silane forming size and glass fiber strands threated therewith for resin reinforcement

Info

Publication number: US3168389A
Application number: US79031A
Authority: US
Inventors: George E Eilerman
Original assignee: Pittsburgh Plate Glass Co
Current assignee: PPG Industries Inc
Priority date: 1960-12-28
Filing date: 1960-12-28
Publication date: 1965-02-02
Anticipated expiration: 1982-02-02
Also published as: BE606417R; GB939466A; DE1157353B

Description

Feb. 2, 1965 G. E. EILERMAN 3,168,389

SILANE FORMING SIZE AND GLASS FIBER STRANDS TREATED THEREWITH FDR RESIN REINFORCEMENT Filed Dec. 28, 1960 INVENTOR.

GEORGE E. EILEBMAN WWW ya United States Patent i 3,168,389 SILANE FGRMING SIZE AND GLASS FIBER STRANDS TREATED THEREWITH FOR RESIN REINFURCEMENT George E. Eilerman, Perrysviile, Pa., assignor to Pittsburgh Plate Glass Company, Pittsburgh, Pa., :1 corporation of Pennsylvania Filed Dec. 28, 1960, Ser. No. 79,031

'13 Claims. (Cl. 65-3) The present invention relates to a glass fiber treatment and it has particular relation-to a size for treating glass fibers which are to be used in various forms as a reinforcement for resins. This application is a continuationin part of my application Serial No. 825,432, filed July 7, 1959, now abandoned.

A glass fiber strand is composed of a multitude of fine glass filaments which are formed by being drawn at a high rate of speed from molten cones of glass located at the tips of small orifices in a bushing such as shown in U.S. Patent No. 2,133,238. During formation, the filaments are coated while moving at a speed of the order of 5,000 to 20,000 feet per minute with a size which contains a binder to give the strand integrity for workability, i.e., for twisting, plying and weaving. If the strand does not have proper integrity, fuzzing occurs during these operations and eventually the strand breaks. The size also contains a lubricant for the filaments to prevent destruction of the strand by abrasion of the individual filaments against each other or against fiber handling equipment.

It is common practice to use glass fiber strands and glass fiber cloth as a reinforcement for resins. For such use, the glass fiber are coated with a coupling agent or finish material which makes the surface of the glass fibers hydrophobic and compatible with the particular resins with which they are to be employed. These coupling agents greatly increase the dry and wet flexural strength of the glass fiber-resin laminate.

A number of silane and siloxane materials have been found to be useful as coupling agents. For example, vinyl and allyl halo, alkoxy, amino or acyloxy silanes, their hydrolysis products and polymers of the hydrolysis products are uitable for such use. Some of the silanes are disclosed in U.S. Patents Nos. 2,563,228; 2,688,006; 2,688,007; 2,723,211; 2,742,378; 2,754,237; 2,776,910 and 2,799,598.

When the glass fibers are used in the form of strand, i.e., roving or chopped strand or twisted strand, for resin reinforcement, the coupling agent is usually combined with the size and applied with the size to the fibers during their attenuation and forming. The size employed is usually an aqueous dispersion of (1) a film-forming, synthetic resin latex made by aqueous emulsion polymerization of an ethylenic monomer, for example, polyvinyl acetate latex, and (2) a textile lubricant or softener. Roving is formed by combining a number of strands in parallel form and winding the strands on a tubular support in a manner such that the combined strands may be unwound and used to form woven roving or chopped strands. made according to conventional textile twisting techniques by removing the strand from the forming package and winding it on a twister bobbin. It is therefore necessary that the strand have good integrity and resistance to Twisted strand (single end on a bobbin) is' 3,168,389 Patented Feb. 2, 1955 fuzzing during the steps employed to make the twisted strand or roving and fabricate them into forms suitable for useas a resin reinforcement.

When roving is woven to form a roving cloth for resin reinforcement, it is necessary that the roving have a certain degree of hardness. The roving should be hard and flexible, but not brittle. If the roving is too soft, it fuzzes in the heddles. When this occurs, the weaving operation must be interrupted to remove the fuzz. If the fuzz is not removed, it causes the woven roving to have loops and holes in it and otherwise be non-uniform.

Ordinarily, when it is desired to make a strand or roving harder for weaving purposes, the procedure is to increase the amount of binder in the size. There is a limit to the amount of binder which can be applied in the size during the formation of the strand because too much binder on the strandwill render the strand diificult to remove from the forming package. It has been found that the use of the maximum allowable amount of binder, such as polyvinyl acetate latex, in a silane-containing size does not render the strand or roving sufficiently hard for some weaving procedures. It is therefore an object of this invention to provide a silane size for application to strands, during their formation to enable the production of a relatively hard roving. The term hard roving means a roving which has good strand integrity and which feels hard to the touch as contrasted to a soft roving which feels soft to the touch.

A further object of this invention is to produce a single type of hard roving which can be used as a reinforcement for different type of resins. Vinyl and allyl silanes have been used to treat glass fibers which are to be combined with styrenated, polyester resins. It is believed by some persons that during polymerization of the resin in situ with the glass fibers, there is a chemical reaction between the unsaturated groups in the resin and the unsaturated groups in the silane coating on the fibers. It is desired that a treatment be provided for glass fiber roving which will render the roving capable of providing an increased flexural strength to glass fiber resin laminates in general and not just to laminates of specific resins. For example, it is desired that a roving be provided which is equally useful as a reinforcement for styrenated polyester resins and epoxy resins. It is obvious that such a versatile roving will reduce the storage and inventory problems of both manufacturers and users of the roving.

An additional object of the invention is to provide glass fiber roving which has been treated with a size containing an alkenyl silane, such as vinyltriacetoxy silane, with good wet out properties. It is desirable in the formation of glass fiber laminates that the resin completely impregnate the strand and wet the surfaces of the fibers as quickly as possible in order to reduce the time required to make the laminates as well as to provide a laminate with maximum possible strength.

It is a further object of this invention to provide a glass fiber strand which is treated with a size containing a coupling agent and which can be twisted, plied and woven into cloth for use as a resin reinforcement without requiring heat cleaning and finishing of the cloth prior to such use as isnow required. 7

These and other objects of the invention are accomplished by treating glass fiber strands during their forma tion with a size containing a binder, a lubricant or softener,

- 30 minutes before being added to the latex.

water is ,then addedto make 250 gallons of sizing solution. The sizing solution as thus prepared has a pH of about an alkenyl acyloxy silane such as vinyltriacetoxy silane and an amino-alkylalkoxy silane such' as gamma-aminopropyl triethoxy silane.

The alkenyl acyloxy silanes contemplated for use in the present invention are illustrated by the following structural formula:

(R1) ..si(0 412) 4-n wherein R is an alkenyl radical selected from the group consisting of vinyl and allyl radicals, R is H or an alkyl or substituted .alkylradical containing'l to carbon atoms audit is a whole number from 1 to 3, preferably 1. Typical examples of the alkenyl acyloxy silanes which are usable in accordance with the present invention are listed below: I

R2 wherein R may be H, an alkyl radical containing 1 to 5 carbon atoms or H[NHCH -CH x being 1 to 5, R

may be H or an alkyl radical containing 1 to 5 carbon atoms, R3 and R4 are alkyl radicals preferably containing 1 to 5 carbon atoms, and n is a whole number from 1 to 3, preferably 1. Typical examples of the amino-alkyl alkoxy silaneinclude gamma-amino-propyl triethoxysilane and similar silanes produced in the manner shown in US. Patent No. 2,832,754.

A typical example of the size is as follows.

Example I Ingredient: ,Parts by weight Aqueousdispersion of polyvinyl acetate latex (55% by weight of solids) 129.1 Pelargonic acid amide solubilizedin water with acetic acid (KL-185a) 5.0 Vinyltriacetoxysilane 1 1.0 Gamma-amino-propyl triethoxysilane 5.5 Water 1942 Two hundred fifty gallons of the glass fiber size can be made by dispersing the polyvinyl acetate latex in about 80 gallons of water in a mixing tank. The textile softener RL-185a is added to about 70 gallons of water maintained at a temperature of about 130 to 160 F. and thoroughly mixed therein. This mixture is then added to the aqueous dispersion of the latex. The vinyltriacetoxysilane and the gamma-amino-propyl triethoxysilane are mixed separately with equal amounts of cold water, added to each other and then added immediately, say for example within ten minutes, to the mixing tank. It has been found that the improvement in Wet-out properties is not obtained if the silane mixture is allowed to stand for too long a time, i.e. Sutficient 4.3 tov 4.7 anda solid content of about 3.5 to 4.1 percent by weight;

It is desirable to add the silanes together in an aqueous a small amount of plasticizer in it.

gamma-amino-propyl triethoxysilane is alkaline and if it is added by. itself, it will tend to precipitate some of the polyvinyl acetate latex from the dispersion.

The sizing solution is applied to the individual fibers during their formation in the manner illustrated in the drawing. The sizing solution is applied to the individual form a strand, by means of a roller applicator 18 which is composed of a rotating roller19 partially submerged in the sizing solution 20 contained in a reservoir 22. Such an applicator is shown in more detail in US. Patent No. 2,728,972. The fibers are grouped into a strand by a graphite guide 24and wound around a forming tube 26 rotatingat approximate 7500 r.p.m. to produce a strand travel of approximately 12,000 to 15,000 feet per minute. Other methods of applying the size to the strand of glass fibers, such as a pad applicator, may be employed and the strand may be formed by means other than Winding on' the forming tube, such as by means of a pair of rotating wheel pullers which direct the strand into a suitable collecting device. The glass fiber strands wound on the forming tube 26 are then dried. This may be done by heating them at a temperature and for a length of time sufiicient to remove substantially all of the water, for example at about 275 F. for 8 hours; This drying causes the silanes to fix themselves to the glass surface and to produce the degree of strand integrity and hardness required for forming the strandginto a woven cloth or woven roving. The solids content of size on the strand averages about 0.5 to 2.0 percent by weight, preferably about 0.75 percent by weight.

The glass fiber size can be made by using other filmforming, glass fiber binders in place of thepolyvinyl acetate latex. .These binders are latices, i.e., aqueous dispersions of synthetic resins made by aqueous emulsion polymerization of 'ethylenic monomers, such as the various acrylates which are esters of acrylic and methacrylic acid and an aliphatic alcohol having 1 to 6 carbon atoms including for example, methyl methacrylate and methyl acrylate. Other ethylenically unsaturated monomers can also be employed to form homopolymeric and copolymeric latices within the purview of this invention, e.g., vinyl chloride, styrene, acrylonitri'le, chlorovinyl acetate, butadiene, vinylidene chloride and various copolymers of the above monomers such as 'butadiene-styrene, butadieneacrylonitrile, vinyl chloride-vinyl acetate copolymers and like materials which can be employed in latex form in aqueous dispersions as binders for glass fiber strands. These latices .generally have an average particle size of 0.1 toS microns.

A plasticizer may be'used in the size with latices which tend to deposit as brittle or discontinuous films although ordinarily aplasticizer is not used for it tends to soften the roving. For example, a plasticizer may be used with latices of polyvinyl acetate, polyvinyl chloride, the poly- .acrylates and polystyrene, Whereas the plasticizer is generally not used with butadiene-styrene latex. Frequently the latex as purchased from the manufacturer will have The plasticizer may be any known plasticizer for the various latices such as dibutyl" phthalate, tricresyl phosphate, dioctyl phthalate, dii'soo'cty'l phthalate and other esters which are conventional- -ly used'as plasticizers. Approximately 1 to 5 percent by weight of the latex on a solid basis is employed in the size. Approximately 0.5 to 5 percent by weight of plasticizer based upon the weight of the solid latex may be employed. Larger amounts may be employed with polyvinyl chloride, polystyrene and polyvinylidene chloride latices if needed for proper-film forming.

The size contains about 0.3 to 2 percent by weight of aualkenyl acyloxy silane such as vinyltriacetoxysilane and about 0.1 to Zpercent by weight of an amino-alkyl alkoxyl silane such as gamma-.amino-propyl triethoxysilane. The amount of vinyltriacetoxysilane is usuallyl to 4 times the amount of gamma-amino-propyl triethoxysilane in the size. Greater than 2 percent by weight of each of the silanes can be used, but larger amounts do not materially increase the flexur-al strength characteristics of the resin laminates. It'is preferred that no more than about 2 percent by weight of the gamma-amino-propyl triethoxysilane be employed because adequate hardness is obtained by such amount. Where exceptionally hard roving is desired, however, greater amounts of the gamma-aminopropyl triethoxysilane may be employed.

The textile softener for use in the present invention is a cationic-active, acid solubilized, fatty acid amide. A suitable material is manufactured by the Arnold Hoffman Company under the trade number Riv-185a. It is an anhydrous material which is a deep reddish, amber, viscous liquid .at room temperature. It is water dispersible and has a pH of 8.9 to 9.4 in a one percent by weight aqueous dispersion. Other commercially available acid solubilized, fatty acid amides are useful as textile softeners imidazolines which may be formed by causing fatty acids to react with polyalkylene polyamines under conditions which produce ring closure. The reaction of .tetraethylene pentamine with stearic .acid is exemplary of such reaction. These imidazolines are described more fully in U.S. Patent No. 2,200,815. Other suitable imidazolines are described in U.S. Patents Nos. 2,267,965; 2,268,273 and 2,355,837.

The size may contain a wetting agent. The wetting agent is preferably cationic or non-ionic and it may also serve as an additional lubricant. Any material which is conventionally known'to be useful as such and will re duce the surface tension of the sizing solution so that it is about 5 to 35 dynes per square centimeter can be used. Such materials include cetyl or stearyl monoamine hydrochloride or acetate, dodecyl amine, hexadecyl amine and secondary and tertiary derivatives of the same, for example, dodecyl methyl amine and salts thereof. Alkyl quaternary ammonium compounds such as trimethyl stearyl or cetyl ammonium bromides .and chlorides and generally any of the amine compounds that dissociate in water systems to provide a positive radical containing a group of more than 8 and preferably 12 or more carbon atoms may be used. Other examples of suitable wetting agents are polyoxyethylene derivatives of a sorbitol fatty acid ester such as polyoxyethylene sorbitan monostearate or polyoxyethy-lene sorbitan trioleate. The amount of such wetting agent employed generally ranges from about 0.01 to 1 percent by weight of the aqueous sizing solution.

The total solids content of the sizing solution is about 2 to 5.5 percent by weight of the solution. In all events the amounts of the various ingredients should not exceed that amount which will cause the viscosity of the solution tobe greater than about 100 centipoises at C. Solutions having a viscosity of greater than 100 centipoises at 20 C. are very difficult to apply to glass fiber strands during their formation Without breaking the strand. It is preferred that the viscosity of the size be between 1 and 20 centipoises at 20 C. for best results. The pH of the solution may vary from about 3 to 8 depending upon the sensitivity of the latex to precipitate from the dispersion. The more sensitive the latex is to precipitation, the higher the pH of the solution. It is desired that 6 the sizing solution have a pH of 4 to 5 when polyvinyl acetate is the latex.

Further examples of the sizing solutions which may be employed in the present invention are listed below.

' This sizing solution is made in the same manner as that in Example I with the melamine formaldehyde resin being added as the final ingredient just prior to the final addition of the water. It has been found that the addition of about 0.3 to 2 percent by weight of melamine formaldehyde to the size serves several purposes. The

strand which is sized with the solution of Example H is whiter in color than the strand sized with the solution of Example I. The melamine formaldehyde resin provides this improved color and does so while slightly decreasing the hardness of the strand thus formed. This is important for the addition of the gamma-amino-propyl triethoxysilane to the size increases the hardness of the strand as well as making it more compatible with epoxy resins. The melamine formaldehyde resin is therefore useful to control the hardness ofthe strand thus produced.

The melamine formaldehyde resin in" the size improves the abrasion resistance of the strand and permits twisting of the strand according to conventional textile twisting and plying techniques without undue breakage of filaments. The twisted strand (yarn) can be woven into cloth and combined with a resin without requiring heat cleaning and finishing of the cloth as has been required in the past. Prior to this invention glass fiber strands which have been twisted into yarn have almost exclusively been sized with a starch-vegetable oil containing size to permit twisting. The starch-oil size had to be burned off after the yarn was woven into cloth and the cloth had to be treated with a silane or chrome finish in order to make the cloth compatible with organic resinous materials.

The size of Example II is applied to the strand in the same manner as described above with respect to the size of Example I and the treated strand is dried as described above and fabricated into various textile products, such as twisted strand, cloth, chopped strand, chopped strand mat, roving and woven roving. Further examples of the sizing solutions which may be applied to glass fibers as described above are as follows.

' 7 Example 111 Ingredient: 1 Parts by weight Butadiene styrene latex (48% by weight solids) 129.1 Vinyltriacetoxysilane 11.0 Gamma-amino-propyl triethoxysilane 5.5 Tetraethylene pentamine amide of stearic acid solubilized in water with meth'acrylic acid 5 .0 Water 1942 Example IV Ingredient: Parts by weight Polymethyl methacrylate latex (40% by weight of solids) 129.1 Vinyltriacetoxysilane l 1.0 Gamma-amino-propyl triethoxysilane 5.5 Textile softener (anhydrous, acid solubilized fatty acid amide) 5.0 Water 1942 The strandswhich have been sized with the solutions are fabricated as described above provide increased flexural strengths to resins reinforced with the strand. 'Glass fiber cloth woven from 60 end roving treated as described in Example H was laminated with a styrenated polyester resin. The cloth was woven on an Axminster loom according to a 1 to 1 pattern resulting in 60' ends 'of 204 filamentE type glass strand (140s) in both the warp and fill. Four plies of the cloth were individually saturated with the resin and then stacked upon each other to insure proper nesting. The resin was a 'polymerizable mixture of a styrenated polyester containing about 2 percent by weight of methyl ethyl ketone peroxide and 3 percentby weight'cobalt; The assembly was cured for several hours at room temperature and atmospheric pressure. The resulting'laminate had about 60 percent by weight of glass and dry flexural strength of 67,700 pounds per square inch.. After a 2-hour immersion in boiling water the flexural strength of the laminate was 60,100 pounds per square inch. 7

The invention is particularly useful when the glass fibers are who used as reinforcement for low pressure thermosetting type resins, for example, unsaturated polyester-ethylenic resins such .as shown in US. PatentNo. 2,676,947, granted to Parker. These resins. are inter- I polymersof, (A) a polyester of a dihydric alcohol such as ethylene glycol, propylene glycol, 1,3-butylene glycol, diethylene glycol, dipropylene glycol and higher polymers of alkylene 'glycols, and an alpha, beta ethylenic, dicarboxylic acid such as maleic or fumaric acid with (B) other polymerizable ethylenic monomers such as styrene, vinyl acetate, vinyl toluene, allyl esters including allyl acetate, allyl succinate, diallyl phthalate, diallyl cyanurate, triallyl cyanurate, dichloro styrene, etc.

The invention is also useful when the glass fibers are to be laminated with other resinous or plastic materials such as polyester or epoxy resins such as condensation 0.1 m2 percent by weight an aminoalkyl alkoxy silane represented by the following structural formula:

wherein R is selected from the group consisting of hydrogen, alkyland H[NHCH CH x being a whole numpolymers of an epihalohydrin and a polyhydroxy phenolic 7 compound and derivatives thereof such as bis-phenol A. Woven roving as described above is saturated with the epoxy resin and meta phenylene diamine. The combination is cured according to conventional epoxy resin curing techniques at an elevated temperature and pressure.

Itwas particularly noted in the preparation of resinous I laminates utilizing glass fiber strand treated with a size containing both an alkenyl acyloxy silane and an aminoalkyl alkoxy silane according to the present invention, that the strands in their various fabricated form, such as cloth, chopped strand mat and woven roving have super-ior wet-out properties as compared to when either of these silanes are used alone in a size in comparable amounts.

Although the present invention has been described with respect to specific details of certain embodiments thereof, it is not intended that such details act as limitations upon the scope of the invention except insofar as set forthin' the accompanying claims.

I claim: Y

1. A method of forming-a glass fiber strand which can be fabricated and laminatedwith a resin which comprises drawing glass streams through orifices in a bushing to form individual glass filaments, movingthe filaments away from the bushing at a high rate of speed and forming them 7 into a strand, applying to the filaments while they are moving at this speed an aqueous sizing solutionconsisting essentially of 1 to 5 percent by weight on a solids basis of a synthetic polymer latex of an ethylenic monomer, 0.3 to 2 percent by weight of an alkenyl acyloxy silane having the following structural formula:

her from 1 to 5, R ,is selected from the group consisting of hydrogen and alkyl, R and R are alkyl and n is a whole number from 1 to 3, and 0.1 to,1 percent by weight of a textile softener, the total solids content of the solution being 2 to 5.5"percent by weight and the viscosity of the solution being less than 100 centipoises at 20 C., and drying the glass fibers so treated.

2. The method of claim 1 wherein the alkenyl acyloxy silane is vinyltriacetoxy silane.

3. The method of 'claim 1 wherein the aminoalkyl 'alkoxy silane is gamma-amino-propyl triethoxy silane.

4. The method of claim 3 wherein the alkenyl acyloxy silane is vinyltriacetoxy silane.

r 5. The method of claim 1 wherein 0.3 to 2 percent by weight of melamine formaldehyde resin is present in the sizing solution.

6. Glass fiber strands formed according to the metho of claim 1.

7. Glass fiber strands formed according to the method ofclaim 2.

' 8. Glass fiber strands formed according to the method of claim 3. n

9. Glass fiber strands formed according to the meth of claim 4. V v w 1 10. Glass fiber strands formed according to the method of claim ,5.

11. A method of forming a glass fiber, reinforced resinous body which comprises forming glass fiber strands bydrawing themfrom molten glass through orifices in a bushing to form individual glass filaments, moving the filaments away fromthe bushing at a high rate of speed and forming the filaments into a strand, applying to the strands during their formation while: they are moving at this speed an aqueous sizing solution which consists essentially of l to 5 percent by weight on a solids basis of a syntheticpolymer latex of an ethylenic monomer, 0.3 to i 2 percent by weight of vinyltriacetoxysilane, 0.1 to 2 percent by' weight of gamma-amino-propyl triethoxysilane and 0.1 to 1 percent by weight of a textile softener, the total solids content of thesolution being 2 to 5.5 percent by weight and the viscosity of the solution being less than 100 centipoises at 20 C., drying the treated strands, fabricating the glass fiber strands into a form suitable for combining with a resin, combining the fabricated strands with a curable resin and curing -the resin to form the reinforced body.

12. The method described in claim 11 wherein the sizing solution contains 0.3 to 2 percent by weight of melamine formaldehyde.

13. An aqueous size for application to glass fiber strands during their format-ion which consists essentially a of lto 5 percent by weight on a solids basis of a synthetic polymer latex of an ethylenic monomer, 0.3 to 2 percent by weight of an alkenyl acyloxy silane having the following structural formula:

wherein R is an. alkenyl radical selected from the group consisting of vinyl and allyl radicals, R is selected from the group consisting of hydrogen and an alkyl radical and n is a whole number from 1 to 3, and dissolved therein represented by the following structural formula:

wherein R is selected from the group consisting of hydrogen, alkyl and H[NHCH CH x being a whole number from 1 to 5, R is selected from the group consisting of hydrogen and alkyl, R and R are alkyl and n is a whole number from 1 to 3, and 0.1 to 1 percent by Weight of a textile softener, the total'solids content of the solu- 0.1 to 2 percent by weight an amino-alkyl alkoxy silane tion being 2 to 5.5 percent by weight and the viscosity of the solution being less than IOO'centipoises at 20 C.

References Cited in the file oi this patent UNITED STATES PATENTS Steinman 'Aug. 31, 1954 'Brooks July '10, 1956 Werner et a1. NOV."19, 1957 Jex et a1. Apr. 29,1958 Hoffman et a1. Apr. 26, 1960 Eilerman AugIl, 1961 Jex et al. July 17, 1962

Claims

1. A METHOD OF FORMING A GLASS FIBER STRAND WHICH CAN BE FABRICATED AND LAMINATED WITH A RESIN WHICH COMPRISES DRAWING GLASS STREAMS THROUGH ORIFICES IN A BUSHING TO FORM INDIVIDUAL GLASS FILAMENTS, MOVING THE FILAMENTS AWAY FROM THE BUSHING AT A HIGH RATE OF SPEED AND FORMING THEM INTO A STRAND, APPLYING TO THE FILAMENTS WHILE THEY ARE MOVING AT THIS SPEED AN AQUEOUS SIZING SOLUTION CONSISTING ESSENTIALLY OF 1 TO 5 PERCENT BY WEIGHT ON A SOLIDS BASIS OF A SYNTHETIC POLYMER LATEX OF AN ETHYLENIC MONOMER, 0.3 TO 2 PERCENT BY WEIGHT OF AN ALKENYL ACYLOXY SILANE HAVING THE FOLLOWING STRUCTURAL FORMULA: