[{"data":1,"prerenderedAt":4804},["ShallowReactive",2],{"blog-\u002Fblog\u002Fcombination-of-errors-calculating-the-propagation-of-uncertainty":3,"blog-surround-\u002Fblog\u002Fcombination-of-errors-calculating-the-propagation-of-uncertainty":4793},{"id":4,"title":5,"author":6,"body":7,"category":4768,"description":4769,"extension":4770,"image":4771,"meta":4772,"navigation":4785,"path":4786,"publishedAt":4787,"readTime":4788,"seo":4789,"sitemap":4790,"stem":4791,"__hash__":4792},"blog\u002Fblog\u002F2.combination-of-errors-calculating-the-propagation-of-uncertainty.md","Combination of Errors: Calculating the Propagation of Uncertainty","Surveyiiing Expert",{"type":8,"value":9,"toc":4747},"minimark",[10,15,29,33,43,47,355,359,1185,1188,1568,1572,1577,2034,2038,2632,2636,2929,2933,3017,3894,3898,4214,4218,4434,4438,4567,4571,4726,4730,4733,4737],[11,12,14],"h2",{"id":13},"overview","Overview",[16,17,18,19,23,24,28],"p",{},"In surveying, we rarely measure the \"final\" answer directly. 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a^n",[25,2665,2667,2685],{"className":2666,"ariaHidden":80},[79],[25,2668,2670,2673,2676,2679,2682],{"className":2669},[84],[25,2671],{"className":2672,"style":1616},[88],[25,2674,1594],{"className":2675},[93,94],[25,2677],{"className":2678,"style":586},[166],[25,2680,392],{"className":2681},[590],[25,2683],{"className":2684,"style":586},[166],[25,2686,2688,2692],{"className":2687},[84],[25,2689],{"className":2690,"style":2691},[88],"height:0.6644em;",[25,2693,2695,2698],{"className":2694},[93],[25,2696,71],{"className":2697},[93,94],[25,2699,2701],{"className":2700},[524],[25,2702,2704],{"className":2703},[528],[25,2705,2707],{"className":2706},[533],[25,2708,2710],{"className":2709,"style":2691},[537],[25,2711,2712,2715],{"style":559},[25,2713],{"className":2714,"style":546},[545],[25,2716,2718],{"className":2717},[550,551,552,553],[25,2719,2660],{"className":2720},[93,94,553],[25,2722,2724,2771],{"className":2723},[53],[25,2725,2727],{"className":2726},[57],[59,2728,2729],{"xmlns":61},[63,2730,2731,2768],{},[66,2732,2733,2739,2741,2743,2745,2747,2760,2766],{},[1293,2734,2735,2737],{},[69,2736,384],{},[69,2738,1594],{},[109,2740,392],{},[109,2742,1756],{},[109,2744,112],{"stretchy":111},[69,2746,2660],{},[394,2748,2749,2751],{},[69,2750,71],{},[66,2752,2753,2755,2757],{},[69,2754,2660],{},[109,2756,1679],{},[388,2758,2759],{},"1",[1293,2761,2762,2764],{},[69,2763,384],{},[69,2765,71],{},[109,2767,138],{"stretchy":111},[73,2769,2770],{"encoding":75},"\\sigma_A = \\pm (n a^{n-1} \\sigma_a)",[25,2772,2774,2829],{"className":2773,"ariaHidden":80},[79],[25,2775,2777,2780,2820,2823,2826],{"className":2776},[84],[25,2778],{"className":2779,"style":1792},[88],[25,2781,2783,2786],{"className":2782},[93],[25,2784,384],{"className":2785,"style":171},[93,94],[25,2787,2789],{"className":2788},[524],[25,2790,2792,2812],{"className":2791},[528,529],[25,2793,2795,2809],{"className":2794},[533],[25,2796,2798],{"className":2797,"style":1811},[537],[25,2799,2800,2803],{"style":1345},[25,2801],{"className":2802,"style":546},[545],[25,2804,2806],{"className":2805},[550,551,552,553],[25,2807,1594],{"className":2808},[93,94,553],[25,2810,573],{"className":2811},[572],[25,2813,2815],{"className":2814},[533],[25,2816,2818],{"className":2817,"style":1364},[537],[25,2819],{},[25,2821],{"className":2822,"style":586},[166],[25,2824,392],{"className":2825},[590],[25,2827],{"className":2828,"style":586},[166],[25,2830,2832,2836,2839,2842,2845,2883,2923],{"className":2831},[84],[25,2833],{"className":2834,"style":2835},[88],"height:1.0641em;vertical-align:-0.25em;",[25,2837,1756],{"className":2838},[93],[25,2840,112],{"className":2841},[155],[25,2843,2660],{"className":2844},[93,94],[25,2846,2848,2851],{"className":2847},[93],[25,2849,71],{"className":2850},[93,94],[25,2852,2854],{"className":2853},[524],[25,2855,2857],{"className":2856},[528],[25,2858,2860],{"className":2859},[533],[25,2861,2863],{"className":2862,"style":538},[537],[25,2864,2865,2868],{"style":559},[25,2866],{"className":2867,"style":546},[545],[25,2869,2871],{"className":2870},[550,551,552,553],[25,2872,2874,2877,2880],{"className":2873},[93,553],[25,2875,2660],{"className":2876},[93,94,553],[25,2878,1679],{"className":2879},[794,553],[25,2881,2759],{"className":2882},[93,553],[25,2884,2886,2889],{"className":2885},[93],[25,2887,384],{"className":2888,"style":171},[93,94],[25,2890,2892],{"className":2891},[524],[25,2893,2895,2915],{"className":2894},[528,529],[25,2896,2898,2912],{"className":2897},[533],[25,2899,2901],{"className":2900,"style":1342},[537],[25,2902,2903,2906],{"style":1345},[25,2904],{"className":2905,"style":546},[545],[25,2907,2909],{"className":2908},[550,551,552,553],[25,2910,71],{"className":2911},[93,94,553],[25,2913,573],{"className":2914},[572],[25,2916,2918],{"className":2917},[533],[25,2919,2921],{"className":2920,"style":1364},[537],[25,2922],{},[25,2924,138],{"className":2925},[195],[25,2927,2928],{},"6",[11,2930,2932],{"id":2931},"step-by-step-example","Step-by-Step Example",[16,2934,2935,2938,2939,3014,3015],{},[363,2936,2937],{},"Problem:"," The three angles of a triangle are measured, each with a standard error of ",[25,2940,2942,2967],{"className":2941},[53],[25,2943,2945],{"className":2944},[57],[59,2946,2947],{"xmlns":61},[63,2948,2949,2964],{},[66,2950,2951,2953],{},[109,2952,1756],{},[394,2954,2955,2957],{},[388,2956,27],{},[66,2958,2959,2962],{},[109,2960,2961],{"mathvariant":131},"′",[109,2963,2961],{"mathvariant":131},[73,2965,2966],{"encoding":75},"\\pm 2''",[25,2968,2970],{"className":2969,"ariaHidden":80},[79],[25,2971,2973,2977,2980],{"className":2972},[84],[25,2974],{"className":2975,"style":2976},[88],"height:0.8352em;vertical-align:-0.0833em;",[25,2978,1756],{"className":2979},[93],[25,2981,2983,2986],{"className":2982},[93],[25,2984,27],{"className":2985},[93],[25,2987,2989],{"className":2988},[524],[25,2990,2992],{"className":2991},[528],[25,2993,2995],{"className":2994},[533],[25,2996,2999],{"className":2997,"style":2998},[537],"height:0.7519em;",[25,3000,3001,3004],{"style":559},[25,3002],{"className":3003,"style":546},[545],[25,3005,3007],{"className":3006},[550,551,552,553],[25,3008,3010],{"className":3009},[93,553],[25,3011,3013],{"className":3012},[93,553],"′′",". What is the total error in the sum of the angles? 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\\gamma",[25,3059,3061,3080,3099,3119],{"className":3060,"ariaHidden":80},[79],[25,3062,3064,3067,3071,3074,3077],{"className":3063},[84],[25,3065],{"className":3066,"style":1616},[88],[25,3068,3039],{"className":3069,"style":3070},[93,94],"margin-right:0.1389em;",[25,3072],{"className":3073,"style":586},[166],[25,3075,392],{"className":3076},[590],[25,3078],{"className":3079,"style":586},[166],[25,3081,3083,3086,3090,3093,3096],{"className":3082},[84],[25,3084],{"className":3085,"style":1635},[88],[25,3087,3044],{"className":3088,"style":3089},[93,94],"margin-right:0.0037em;",[25,3091],{"className":3092,"style":790},[166],[25,3094,430],{"className":3095},[794],[25,3097],{"className":3098,"style":790},[166],[25,3100,3102,3106,3110,3113,3116],{"className":3101},[84],[25,3103],{"className":3104,"style":3105},[88],"height:0.8889em;vertical-align:-0.1944em;",[25,3107,3049],{"className":3108,"style":3109},[93,94],"margin-right:0.0528em;",[25,3111],{"className":3112,"style":790},[166],[25,3114,430],{"className":3115},[794],[25,3117],{"className":3118,"style":790},[166],[25,3120,3122,3126],{"className":3121},[84],[25,3123],{"className":3124,"style":3125},[88],"height:0.625em;vertical-align:-0.1944em;",[25,3127,3054],{"className":3128,"style":654},[93,94],[1192,3130,3131,308,3134],{},[363,3132,3133],{},"Standard Errors:",[25,3135,3137,3183],{"className":3136},[53],[25,3138,3140],{"className":3139},[57],[59,3141,3142],{"xmlns":61},[63,3143,3144,3180],{},[66,3145,3146,3152,3154,3160,3162,3168,3170],{},[1293,3147,3148,3150],{},[69,3149,384],{},[69,3151,3044],{},[109,3153,392],{},[1293,3155,3156,3158],{},[69,3157,384],{},[69,3159,3049],{},[109,3161,392],{},[1293,3163,3164,3166],{},[69,3165,384],{},[69,3167,3054],{},[109,3169,392],{},[394,3171,3172,3174],{},[388,3173,27],{},[66,3175,3176,3178],{},[109,3177,2961],{"mathvariant":131},[109,3179,2961],{"mathvariant":131},[73,3181,3182],{"encoding":75},"\\sigma_\\alpha = \\sigma_\\beta = \\sigma_\\gamma = 2''",[25,3184,3186,3241,3297,3352],{"className":3185,"ariaHidden":80},[79],[25,3187,3189,3192,3232,3235,3238],{"className":3188},[84],[25,3190],{"className":3191,"style":1792},[88],[25,3193,3195,3198],{"className":3194},[93],[25,3196,384],{"className":3197,"style":171},[93,94],[25,3199,3201],{"className":3200},[524],[25,3202,3204,3224],{"className":3203},[528,529],[25,3205,3207,3221],{"className":3206},[533],[25,3208,3210],{"className":3209,"style":1342},[537],[25,3211,3212,3215],{"style":1345},[25,3213],{"className":3214,"style":546},[545],[25,3216,3218],{"className":3217},[550,551,552,553],[25,3219,3044],{"className":3220,"style":3089},[93,94,553],[25,3222,573],{"className":3223},[572],[25,3225,3227],{"className":3226},[533],[25,3228,3230],{"className":3229,"style":1364},[537],[25,3231],{},[25,3233],{"className":3234,"style":586},[166],[25,3236,392],{"className":3237},[590],[25,3239],{"className":3240,"style":586},[166],[25,3242,3244,3247,3288,3291,3294],{"className":3243},[84],[25,3245],{"className":3246,"style":1323},[88],[25,3248,3250,3253],{"className":3249},[93],[25,3251,384],{"className":3252,"style":171},[93,94],[25,3254,3256],{"className":3255},[524],[25,3257,3259,3280],{"className":3258},[528,529],[25,3260,3262,3277],{"className":3261},[533],[25,3263,3266],{"className":3264,"style":3265},[537],"height:0.3361em;",[25,3267,3268,3271],{"style":1345},[25,3269],{"className":3270,"style":546},[545],[25,3272,3274],{"className":3273},[550,551,552,553],[25,3275,3049],{"className":3276,"style":3109},[93,94,553],[25,3278,573],{"className":3279},[572],[25,3281,3283],{"className":3282},[533],[25,3284,3286],{"className":3285,"style":1411},[537],[25,3287],{},[25,3289],{"className":3290,"style":586},[166],[25,3292,392],{"className":3293},[590],[25,3295],{"className":3296,"style":586},[166],[25,3298,3300,3303,3343,3346,3349],{"className":3299},[84],[25,3301],{"className":3302,"style":1323},[88],[25,3304,3306,3309],{"className":3305},[93],[25,3307,384],{"className":3308,"style":171},[93,94],[25,3310,3312],{"className":3311},[524],[25,3313,3315,3335],{"className":3314},[528,529],[25,3316,3318,3332],{"className":3317},[533],[25,3319,3321],{"className":3320,"style":1342},[537],[25,3322,3323,3326],{"style":1345},[25,3324],{"className":3325,"style":546},[545],[25,3327,3329],{"className":3328},[550,551,552,553],[25,3330,3054],{"className":3331,"style":654},[93,94,553],[25,3333,573],{"className":3334},[572],[25,3336,3338],{"className":3337},[533],[25,3339,3341],{"className":3340,"style":1411},[537],[25,3342],{},[25,3344],{"className":3345,"style":586},[166],[25,3347,392],{"className":3348},[590],[25,3350],{"className":3351,"style":586},[166],[25,3353,3355,3358],{"className":3354},[84],[25,3356],{"className":3357,"style":2998},[88],[25,3359,3361,3364],{"className":3360},[93],[25,3362,27],{"className":3363},[93],[25,3365,3367],{"className":3366},[524],[25,3368,3370],{"className":3369},[528],[25,3371,3373],{"className":3372},[533],[25,3374,3376],{"className":3375,"style":2998},[537],[25,3377,3378,3381],{"style":559},[25,3379],{"className":3380,"style":546},[545],[25,3382,3384],{"className":3383},[550,551,552,553],[25,3385,3387],{"className":3386},[93,553],[25,3388,3013],{"className":3389},[93,553],[1192,3391,3392,3395],{},[363,3393,3394],{},"Calculation:",[25,3396,3398,3455],{"className":3397},[53],[25,3399,3401],{"className":3400},[57],[59,3402,3403],{"xmlns":61},[63,3404,3405,3452],{},[66,3406,3407,3413,3415,3417,3443,3445,3447],{},[1293,3408,3409,3411],{},[69,3410,384],{},[69,3412,3039],{},[109,3414,392],{},[109,3416,1756],{},[1758,3418,3419],{},[66,3420,3421,3427,3429,3435,3437],{},[394,3422,3423,3425],{},[388,3424,27],{},[388,3426,27],{},[109,3428,430],{},[394,3430,3431,3433],{},[388,3432,27],{},[388,3434,27],{},[109,3436,430],{},[394,3438,3439,3441],{},[388,3440,27],{},[388,3442,27],{},[109,3444,392],{},[109,3446,1756],{},[1758,3448,3449],{},[388,3450,3451],{},"12",[73,3453,3454],{"encoding":75},"\\sigma_T = \\pm \\sqrt{2^2 + 2^2 + 2^2} = \\pm 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a",[25,4252,4254,4272,4290],{"className":4253,"ariaHidden":80},[79],[25,4255,4257,4260,4263,4266,4269],{"className":4256},[84],[25,4258],{"className":4259,"style":1635},[88],[25,4261,71],{"className":4262},[93,94],[25,4264],{"className":4265,"style":790},[166],[25,4267,2060],{"className":4268},[794],[25,4270],{"className":4271,"style":790},[166],[25,4273,4275,4278,4281,4284,4287],{"className":4274},[84],[25,4276],{"className":4277,"style":1635},[88],[25,4279,71],{"className":4280},[93,94],[25,4282],{"className":4283,"style":790},[166],[25,4285,2060],{"className":4286},[794],[25,4288],{"className":4289,"style":790},[166],[25,4291,4293,4296],{"className":4292},[84],[25,4294],{"className":4295,"style":89},[88],[25,4297,71],{"className":4298},[93,94]," is different from ",[25,4301,4303,4321],{"className":4302},[53],[25,4304,4306],{"className":4305},[57],[59,4307,4308],{"xmlns":61},[63,4309,4310,4318],{},[66,4311,4312],{},[394,4313,4314,4316],{},[69,4315,71],{},[388,4317,42],{},[73,4319,4320],{"encoding":75},"a^3",[25,4322,4324],{"className":4323,"ariaHidden":80},[79],[25,4325,4327,4330],{"className":4326},[84],[25,4328],{"className":4329,"style":538},[88],[25,4331,4333,4336],{"className":4332},[93],[25,4334,71],{"className":4335},[93,94],[25,4337,4339],{"className":4338},[524],[25,4340,4342],{"className":4341},[528],[25,4343,4345],{"className":4344},[533],[25,4346,4348],{"className":4347,"style":538},[537],[25,4349,4350,4353],{"style":559},[25,4351],{"className":4352,"style":546},[545],[25,4354,4356],{"className":4355},[550,551,552,553],[25,4357,42],{"className":4358},[93,553],". In ",[25,4361,4363,4380],{"className":4362},[53],[25,4364,4366],{"className":4365},[57],[59,4367,4368],{"xmlns":61},[63,4369,4370,4378],{},[66,4371,4372],{},[394,4373,4374,4376],{},[69,4375,71],{},[388,4377,42],{},[73,4379,4320],{"encoding":75},[25,4381,4383],{"className":4382,"ariaHidden":80},[79],[25,4384,4386,4389],{"className":4385},[84],[25,4387],{"className":4388,"style":538},[88],[25,4390,4392,4395],{"className":4391},[93],[25,4393,71],{"className":4394},[93,94],[25,4396,4398],{"className":4397},[524],[25,4399,4401],{"className":4400},[528],[25,4402,4404],{"className":4403},[533],[25,4405,4407],{"className":4406,"style":538},[537],[25,4408,4409,4412],{"style":559},[25,4410],{"className":4411,"style":546},[545],[25,4413,4415],{"className":4414},[550,551,552,553],[25,4416,42],{"className":4417},[93,553],", the variables are ",[20,4420,4421],{},"not"," independent, so you cannot use the square-root-sum-of-squares rule ",[25,4424,2631],{},[1192,4426,4427,4430,4431,28],{},[363,4428,4429],{},"Ignoring Units:"," Ensure all standard errors are in the same units (e.g., meters or seconds) before plugging them into the variance equation ",[25,4432,4433],{},"8",[11,4435,4437],{"id":4436},"best-practices","Best Practices",[16,4439,4440,4441,4444,4445,4564,4565,28],{},"Always describe measured data using both the ",[363,4442,4443],{},"Standard Deviation (S)"," of the set and the ",[363,4446,4447,4448,138],{},"Standard Error (",[25,4449,4451,4476],{"className":4450},[53],[25,4452,4454],{"className":4453},[57],[59,4455,4456],{"xmlns":61},[63,4457,4458,4473],{},[66,4459,4460],{},[1293,4461,4462,4465],{},[69,4463,4464],{},"S",[4466,4467,4468,4470],"mover",{"accent":80},[69,4469,115],{},[109,4471,4472],{},"ˉ",[73,4474,4475],{"encoding":75},"S_{\\bar{x}}",[25,4477,4479],{"className":4478,"ariaHidden":80},[79],[25,4480,4482,4485],{"className":4481},[84],[25,4483],{"className":4484,"style":4107},[88],[25,4486,4488,4492],{"className":4487},[93],[25,4489,4464],{"className":4490,"style":4491},[93,94],"margin-right:0.0576em;",[25,4493,4495],{"className":4494},[524],[25,4496,4498,4556],{"className":4497},[528,529],[25,4499,4501,4553],{"className":4500},[533],[25,4502,4505],{"className":4503,"style":4504},[537],"height:0.2474em;",[25,4506,4508,4511],{"style":4507},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[25,4509],{"className":4510,"style":546},[545],[25,4512,4514],{"className":4513},[550,551,552,553],[25,4515,4517],{"className":4516},[93,553],[25,4518,4521],{"className":4519},[93,4520,553],"accent",[25,4522,4524],{"className":4523},[528],[25,4525,4527],{"className":4526},[533],[25,4528,4531,4540],{"className":4529,"style":4530},[537],"height:0.5678em;",[25,4532,4534,4537],{"style":4533},"top:-2.7em;",[25,4535],{"className":4536,"style":546},[545],[25,4538,115],{"className":4539},[93,94,553],[25,4541,4542,4545],{"style":4533},[25,4543],{"className":4544,"style":546},[545],[25,4546,4550],{"className":4547,"style":4549},[4548],"accent-body","left:-0.2222em;",[25,4551,4472],{"className":4552},[93,553],[25,4554,573],{"className":4555},[572],[25,4557,4559],{"className":4558},[533],[25,4560,4562],{"className":4561,"style":1364},[537],[25,4563],{}," of the mean to provide a complete picture of precision ",[25,4566,4433],{},[11,4568,4570],{"id":4569},"faq","FAQ",[4572,4573,4574,4717],"accordion",{},[4575,4576,4578],"accordion-item",{"label":4577},"Is Standard Deviation the same as Standard Error?",[16,4579,4580,4581,4609,4610,4714,4715,28],{},"No. Standard deviation (",[25,4582,4584,4597],{"className":4583},[53],[25,4585,4587],{"className":4586},[57],[59,4588,4589],{"xmlns":61},[63,4590,4591,4595],{},[66,4592,4593],{},[69,4594,4464],{},[73,4596,4464],{"encoding":75},[25,4598,4600],{"className":4599,"ariaHidden":80},[79],[25,4601,4603,4606],{"className":4602},[84],[25,4604],{"className":4605,"style":1616},[88],[25,4607,4464],{"className":4608,"style":4491},[93,94],") measures the spread of individual observations. Standard error (",[25,4611,4613,4634],{"className":4612},[53],[25,4614,4616],{"className":4615},[57],[59,4617,4618],{"xmlns":61},[63,4619,4620,4632],{},[66,4621,4622],{},[1293,4623,4624,4626],{},[69,4625,4464],{},[4466,4627,4628,4630],{"accent":80},[69,4629,115],{},[109,4631,4472],{},[73,4633,4475],{"encoding":75},[25,4635,4637],{"className":4636,"ariaHidden":80},[79],[25,4638,4640,4643],{"className":4639},[84],[25,4641],{"className":4642,"style":4107},[88],[25,4644,4646,4649],{"className":4645},[93],[25,4647,4464],{"className":4648,"style":4491},[93,94],[25,4650,4652],{"className":4651},[524],[25,4653,4655,4706],{"className":4654},[528,529],[25,4656,4658,4703],{"className":4657},[533],[25,4659,4661],{"className":4660,"style":4504},[537],[25,4662,4663,4666],{"style":4507},[25,4664],{"className":4665,"style":546},[545],[25,4667,4669],{"className":4668},[550,551,552,553],[25,4670,4672],{"className":4671},[93,553],[25,4673,4675],{"className":4674},[93,4520,553],[25,4676,4678],{"className":4677},[528],[25,4679,4681],{"className":4680},[533],[25,4682,4684,4692],{"className":4683,"style":4530},[537],[25,4685,4686,4689],{"style":4533},[25,4687],{"className":4688,"style":546},[545],[25,4690,115],{"className":4691},[93,94,553],[25,4693,4694,4697],{"style":4533},[25,4695],{"className":4696,"style":546},[545],[25,4698,4700],{"className":4699,"style":4549},[4548],[25,4701,4472],{"className":4702},[93,553],[25,4704,573],{"className":4705},[572],[25,4707,4709],{"className":4708},[533],[25,4710,4712],{"className":4711,"style":1364},[537],[25,4713],{},") measures the precision of the calculated mean ",[25,4716,4433],{},[4575,4718,4720],{"label":4719},"Can you eliminate error entirely?",[16,4721,4722,4723,28],{},"No. The \"true value\" of a measurement is never known. We can only assess the \"most probable value\" and its reliability ",[25,4724,4725],{},"9, 10",[11,4727,4729],{"id":4728},"conclusion","Conclusion",[16,4731,4732],{},"Error propagation is the \"quality control\" of surveying. By applying the general variance equation, you can ensure that your final deliverables—whether they are property boundaries or bridge coordinates—stay within the required tolerances.",[11,4734,4736],{"id":4735},"references","References",[16,4738,4739,4740,4743,4744,28],{},"Schofield, W. (2001). ",[20,4741,4742],{},"Engineering Surveying",". 5th ed. Butterworth-Heinemann. ",[25,4745,4746],{},"2, 4-12",{"title":4748,"searchDepth":4749,"depth":4749,"links":4750},"",2,[4751,4752,4753,4754,4755,4761,4762,4763,4764,4765,4766,4767],{"id":13,"depth":4749,"text":14},{"id":31,"depth":4749,"text":32},{"id":45,"depth":4749,"text":46},{"id":357,"depth":4749,"text":358},{"id":1570,"depth":4749,"text":1571,"children":4756},[4757,4759,4760],{"id":1575,"depth":4758,"text":1576},3,{"id":2036,"depth":4758,"text":2037},{"id":2634,"depth":4758,"text":2635},{"id":2931,"depth":4749,"text":2932},{"id":3896,"depth":4749,"text":3897},{"id":4216,"depth":4749,"text":4217},{"id":4436,"depth":4749,"text":4437},{"id":4569,"depth":4749,"text":4570},{"id":4728,"depth":4749,"text":4729},{"id":4735,"depth":4749,"text":4736},"Surveying Math","How to mathematically determine the total error in derived surveying quantities like areas, volumes, and coordinates.","md","\u002Fimages\u002Ferror-propagation.jpg",{"authorCredentials":4773,"authorBio":4774,"tags":4775,"sources":4780},"LS","Specialist in geomatics and error analysis.",[4776,4777,4778,4779],"Error Analysis","Math","Precision","Statistics",[4781],{"title":4782,"type":4783,"note":4784},"Engineering Surveying (Fifth Edition)","Book","Primary source for the General Equation of Variance.",true,"\u002Fblog\u002Fcombination-of-errors-calculating-the-propagation-of-uncertainty","2024-03-21",10,{"title":5,"description":4769},{"loc":4786},"blog\u002F2.combination-of-errors-calculating-the-propagation-of-uncertainty","JYg8ACoouz0T-eAwj3ZakzFcI4cEAjJf0E_EcNBDAog",[4794,4799],{"title":4795,"path":4796,"stem":4797,"description":4798,"children":-1},"The Weisbach Triangle: Mastering Orientation via Single-Shaft Correlation","\u002Fblog\u002Fthe-weisbach-triangle-mastering-orientation-via-single-shaft-correlation","blog\u002F1.the-weisbach-triangle-mastering-orientation-via-single-shaft-correlation","A technical guide to orienting underground surveys from a single shaft using the Weisbach triangle method.",{"title":4800,"path":4801,"stem":4802,"description":4803,"children":-1},"Rankine’s Method: The Definitive Guide to Setting Out Circular Curves","\u002Fblog\u002Frankines-method-the-definitive-guide-to-setting-out-circular-curves","blog\u002F3.rankines-method-the-definitive-guide-to-setting-out-circular-curves","A step-by-step technical guide to setting out horizontal circular curves using deflection angles and a theodolite.",1783851952013]